Useful Information for Review Assignment 1

Useful Information for Review Assignment 1

pp. 23-4

28) a) A graph represents a function if it passes the vertical line test. This test determines if there is any x –value that corresponds to more than one y- value.

b) A function has an inverse if it passes the horizontal line test. This test determines if there is any y –value that corresponds to more than one x- value.

29 c) Zeros are the x – coordinates of x – intercepts.

30) To solve an exponential equation you take the log of both sides. You should use a log with a base that is the same as that of the exponential function so that the inverse property applies and the functions undo each other. See below for an example.

153x=60

3x=4

log33x=log34

x=log34 [This is because of the inverse property]

x=log104log103 [This is because of the change of base property]

x≈1.262

31) Instead of “rewrite in standard polynomial form” they could’ve just said “expand (or multiply) and simplify”

32) When you want to write an equation for a line, you need to know the slope and a point that the line passes through. See the example below.

A line has a slope of 3 and passes through (-1, 4).

y=3x+b

4=3(-1)+b

4=-3+b

7=b

y=3x+7

If you are not given the slope but are given two points instead, the slope can be found using the formula m=y2-y1x2-x1. If a line is parallel to a given line, it has the same slope as that line.

pp. 50-1

31) b) Zeros are the x – coordinates of x – intercepts. To find them, set the equation equal to zero and solve by factoring.

c) Do not try to do this algebraically! Use the zeros that you found in part b and the fact that you know this parabola opens up to sketch a graph. Then use the graph to determine for which x -values the y-values of the function will be greater than zero.

d) Set the function equal to 10. Subtract 10 from both sides. Factor and solve.

34) Instead of “rewrite each expression as a product of linear factors” they could’ve just said “factor”.

35) 360o = 2п radians = 1 revolution

36) x-n=1xn, so if you have something in the numerator with a negative power, you move it to the denominator with a positive power. If you have something in the denominator with a negative power it can be moved to the numerator with a positive power.