Question

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.

Answer 1

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

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.

Answer 2

Answer:

C: The line of g(x) is steeper and has a lower y-int.

Step-by-step explanation:

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