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Ch.3 Study Guide Video

Added Nov 06, 2019 •

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hello everyone this is it chapter 3 study guide on the first question find the domain and the range of the graph in here were given the set of points on the graph it's probably best actually right down the corner Ceviche one that asks, why so I'm the first one in 00 the second one is going to be one, negative one you write the X first the next is going to be too, negative 2 and then the last one is 3, negative 3 so now when we get our domain or domain is going to be all of our exes so our axes are 0 1 2 and 3 so that's our domain 0 1 2 3 so it should be letter but let's check the range just to make sure are range value should be 0 negative one negative to negative 3 and that's it for the range is just in the reverse order so let her be hey number two we really haven't done a lot what does the domain is remember the exes and we're going you want to look on the x-axis okay that the lowest at is that -4 the biggest taxes. to do you hit every x value between -4 and 2 the only one that matches that really is letter A because of the letter B looks the same but it doesn't have equal bars but here we have closed at the so you would consider the endpoints that you're equal to so there's a thing every x value in between -4 and 2 which is the Y value do we want to look from the like the bottom the top so the lowest y value is -4 the highest y value is positive for so it's going to range from -4 to positive for so letter A number 3 determine whether the relation is a function so we want to make sure that each input is only going to one output member that idea with the with the darts that each Dart can laying in one spot I can't split and Lena to split places so dark 9 is going to 17 is going to 25 is going to 23 is going to three ones going to 4 so there's no doubles on the axis of this is the function and we can say each and put is going to one output okay no no before we have a set of points here is a table here says that appoints five is going to four wheeling to make sure there's not another five 3 is going to 10 but then 3 is going to 8 so that's like dirt number three going to to spot this is not a function x equals 3 going to two different outside number 5 evaluate the function when x equals negative 1 0 and 4 so we're given that remember that's really the domain you want to find the range values the wife so we're going to plug in negative one for x lb + -1 is equal to -2 * -1 - 4 going to multiply first so you get to -4 is -2 so be a negative one is negative to remember this just stands for the Y value at -1 so this would be the coordinate point negative one negative 2 okay now it's plug 0 lb is 0 is -2 * 0 - 4 you get 0-4 which is -4 so this would be the point 0, negative 4 axis zero why is -4 and the last one forget to plug in for Sophia for you couldn't do -2 * 4 - 4 x 4 you add or subtract so negative 8 -4 is -12 okay number 6 values but a different so we're going to find H of -1 first which is absolute value of negative negative 1 so it's the opposite of negative one is going to end up being a pi positive one + 5 so negative negative one is going to become positive one plus five do the inside of the absolute value first 1 + 5 is 6 and then what the absolute value which is  so we wouldn't leave our answer is absolute value bars we would just write 6 so age of -1 is equal to 6 and we're going to plug into Euro so age of zero so negative zero still going to be zero and then 0 + 5 is 5 so absolute value of 5 is just 5 so into 0 oz equal to 5 last one running out of room here plugin for so you'd have -4 + 5 so -4 + 5 is 1 and then absolute value of one is just one so aged of 4 is 1 and I need to -1 to 6 and then ages Heroes 5 okay now 788 is the opposite you want to find act so that the function has the given value so you're given the Y value J of x equals negative 5 Surrey to plug that in over here Sony what is 5 is equal to 3 - x solve for x since the x is negative over here I'm going to add X to make it a positive so we'll have x - 5 equals and then we can add five so we get x equals 8 the wind that Jay of Acts that's really just why is -5 you get 8 for x okay number 8 now we're given that the Y value T of X is equal to one half so we're going to play that in over here so 1/2 is equal to 2x - 4 I'm going to add for to the other side we have four and a half it won't really help us when we divide by 2 to leave it like four and a half I'm going to change this to 4 * 2 is 8 1899 / 2 which is the same thing as equal to 2X and then divided by two that we don't want to divide by 2 so the same thing as multiplying by a half to buy my two is the same as multiplying by 1/2 we get X is equal to 9 * 1 is 9 / 4 9/4 and that's the first page not a second page the table shows the cost per hour to rent a canoe so the number of hours and the rental fee and we want to find me at the function which one matches up we plug in 1 for 8 will that give us 15 if we plug in Wonder this first one 5 * 1 is 5 + 10 okay that's 15 that works good plug in the next 1 5 * 2 is 10 another 10 gives you 20 even just kind of showing that first one 3 * 3 * 5 is 15 plus another 10 is 25 so it's really looking like a worse that was kind of just by the Guess and check method but you definitely want to you know try to see if you can do some of these without looking at the solution first to look at okay well you know what are we have to get i n out if we plug in 1 how do we get 15 if we plug into how do we get 20 so we can see the pattern 1520 2530 so we know if we were to plug in 03 were to go backwards and it's adding five down here we're going to subtract 500 would have to be 10 that's kind of like your it's your your y-intercept 0 is equal to 10 your soap is 5 okay number 10 find the X and Y intercepts of the graph and then graph using intercepts you do had to questions like this on the test to I'm so afraid the x intercept remember you plug-in 0 for the opposite variable so we're going to plug in 0 for a y 2 + 3 * 0 is equal to 602 times anything is zero so that goes away to X is equal to 6 / 2/3 that means the x intercept is 310 when Y is 0 access 3 so we can plot that right here there's the x intercept and then the y-intercept we're going to plug in 0 for x that's going to be 2 * 0 + 3y is equal to 6 that goes away 3 yd equals is 6 / 3y is too low for the Wii plugged in 0 the y-intercept is to Hertz on the y-axis 02 and then you're going to connect it and there's your graph that a graph with a negative slope cuz it's decreasing let's look at the another one Sunday 1 find the x intercept 704 Wiseau to X is equal to -10 I'm just skipping that stuff for you that's going to go 2-0 anyways 0 times anything is gyro divided by 2 so X is -5 so we have the point when y 0 x is -5 I'm not going to have enough room on this graph I'm so the x intercept is going to the here to negative to negative three negative four- five I'm just going to make my own that's over here and then let's find the y intercept a plug-in 0 for x that's going to go to zero so we're going to be left with -3 Y is equal to -10 divided by -3 negative divided by negative is a positive so you get 10/3 star war 0 ax you get 10/3 now when you're playing on the graph that might be better to have either a decimal or a mixed number for this weekend and know where that is so 3 * 3 + 9 with one left over so that's three and a third on the y-axis you're going to go a little bit past 3 and then once you have those two points then you're going to connect them and this is a graph with a positive slope is increasing as we go left to right hey number 12 Graph the linear equation using Y equals MX plus b so it solve for y so let's write down our slope is negative 2/3 remember if it's not a fraction you want to make it a fraction or y-intercept is one and remember that's our y intercept so there's our P value our Y intercept and then from here and let's write down the definition rise over run you go that's our change in y over change in X so you're going to go down to and then to the right three and remember this has a negative slope so it should be going down as you go left to right at 2 1 2 3 to the you want to go back with it as many as you can and then connect it Phoenix question number 13 in y equals MX plus b form no notice there's no number in front but remember there's an invisible one there so RM is 1 / 1 -3 * y intercept van Ry access were down at -3 and then our self is 1/1 and this should be a positive so but you be going as we go left to right up one over one and go in the opposite direction and then connect it a number 14 x equals negative 4 let me see why can be anything but the x value is always going to be here is -4 time here so this is our vertical remember our slope for a vertical line is undefined and there is no y intercept a number 15 in front other than that negative sign for desk has the same as negative one so RM -1 / 1 RBS 3 or Y intercept so we're going to start up here y-intercept is 3D going down as we go left to right so down one so remember this is rise run down one to the right one down into the right should be going down as we go to the right or we can go up one into the last one okay question 16 so the rate of change which is the slope is constant in the graph so consult means call Ian find the rate of change explain what the rate of change means for the situation to remember the slope is rise over run changing your y value over changing your ex value I sure if I talked about this in class but that little a little triangle means the change in your why the difference in your wise okay so the rise in this case our y value is right. The amount of money and are accidents talking about the years and I'm not sure exactly what resale value of a of a refrigerator so what's the rate of change so if find two points on the graph so brand sent from 400 to 300 it dropped a hundred so went down a hundred and then I went over 3 years you are slope with d a hundred over three and even if we pick different points from 300 to 200 dropped a hundred and then it went over from 3 601 / another 3 years you can check your eyes over here run -100 / 3 so the value drops a hundred dollars every 3 years letter b number 17 the points represented by the table while in a line find the slope of the line okay so really to find this food so you can make a graph and check your kind of like what we did with this graph you can definitely do that here another way to do it is to do the subtraction so why chew - y1 over X2 X1 stuff you pick two points I kind of like putting on the as a coordinate point so it doesn't matter which ones you pick and I'll pick -5 and 7 and I'll pick the next one negative three, four I'm going to make this one of my first point so X1 and y1 and this one my second point so asked you in like two does the track your wise so for my versatrack your access -3 no be careful with the negative times negative 3 minus a negative 5 so at the top 4 subtract 7 is -3 now this is going to change to a positive or negative which is too so now you're 3 / 2 laugh and write the slope intercept form of the equation of the line we need to find let's label from this graph the slope and the y-intercept will wear that cross the y-axis that crosses at negative one so that means B is -1 okay we got two points on the graph so let's see if we go up one two three four five six so I Rise is going to be sick and I run is going to be one too we can simplify that what's 6 divided by 2 and 3/4 slope is 3 Barbie value for y intercept never spoke with just three so y equals MX plus b should be Y is equal to 3 X - 1 which is a the number 19 describe the slope of the line so the slope of any horizontal line is 0 I remember when we check the rise over the Run K doesn't go up or down so that would be zero the run it goes over 1 2 3 4 but 0 / everything and Ciara question number 20 of vertical line has an undefined slope and when you check the rise over the Run well if you go from the bottom to the top it went up 1 2 3 4 5 left to right we cannot divide by zero so that undefined and then the last one I'm so 21 so when we look at that line let's say okay is it negative or positive so we always go left to right we read a page left to right it's going down it's decreasing so it's definitely has to be negative so it's not going to be positive and then remember we want to check the ride up or down up or down over the Run left or right so we're going down one and I rise in town one and then 1234 / 4 all rise over run is negative one fourth letter z

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