Directions: Select a single answer choice.
Question 1:
If 5x + 32 = 4 - 2x what is the value of x?
A. - 4
B. - 3
C. 4
D. 7
E. 12
Explanation:
Solving the equation for x, one will get 7x = - 28 and so x = -4 the correct answer is Choice A, -4
Question 2:
The figure above shows the graph of the function f, defined by f(x) = |2x|+ 4 for all numbers x. For which of the following functions g, defined for all numbers x, does the graph of g intersect the graph of f?
A. g(x) = x - 2
B. g(x) = x + 3
C. g(x) = 2x -2
D. g(x) = 2x + 3
E. g(x) = 3x - 2
Explanation:
One can see that all five choices are linear functions whose graphs are lines with various slopes and y-intercepts. The graph of Choice A is a line with slope 1 and y-intercept -2 shown in.
It is clear that this line will not intersect the graph of f to the left of the y-axis. To the right of the y-axis, the graph of f is a line with slope 2, which is greater than slope 1. Consequently, as the value of x increases, the value of y increases faster for f than for g, and therefore the graphs do not intersect to the right of the y-axis. Choice B is similarly ruled out. Note that if the y-intercept of either of the lines in Choices A and B were greater than or equal to 4 instead of less than 4, they would intersect the graph off.
Choices C and D are lines with slope 2 and y-intercepts less than 4. Hence, they are parallel to the graph of f (to the right of the y-axis) and therefore will not intersect it. Any line with a slope greater than 2 and a y-intercept less than 4, like the line in Choice E, will intersect the graph of f (to the right of the y-axis).The correct answer is Choice E, g(x) = 3x – 2.