MATH SOLVE

4 months ago

Q:
# Timmy writes the equation f(x) = 1/4x – 1. He then doubles both of the terms on the right side to create the equation g(x) = x – 2. How does the graph of g(x) compare to the graph of f(x)? The line of g(x) is steeper and has a higher y-intercept. The line of g(x) is less steep and has a lower y-intercept. The line of g(x) is steeper and has a lower y-intercept. The line of g(x) is less steep and has a higher y-intercept.

Accepted Solution

A:

Note that if [tex]\displaystyle{ f(x)= \frac{1}{4} x-1[/tex], and if Timmy doubles both terms, the new function becomes [tex]\displaystyle{ g(x)= \frac{1}{2} x-2[/tex].

The y-intercepts are the points of the graph of the functions where the x-coordinate is 0. So we find the y-intercepts of f(x) and g(x) as follows:

f(0)=-1, and g(0)=-2. Thus the y-intercept of g is lower.

The steepness of each line is determined by the coefficient of x: the larger the coefficient, the steeper the line.

Thus, since 1/2>1/4, the line g(x) is steeper.

Answer: The line of g(x) is less steep and has a lower y-intercept.

The y-intercepts are the points of the graph of the functions where the x-coordinate is 0. So we find the y-intercepts of f(x) and g(x) as follows:

f(0)=-1, and g(0)=-2. Thus the y-intercept of g is lower.

The steepness of each line is determined by the coefficient of x: the larger the coefficient, the steeper the line.

Thus, since 1/2>1/4, the line g(x) is steeper.

Answer: The line of g(x) is less steep and has a lower y-intercept.