Question

The linear parent function, f(x) = x, is transformed to g(x)=3x-2. Which statement correctly compares the graphs of the functions?

Answer 1

In general, the greater the slope of a line, the steeper it is.

On the other hand, the slope-intercept form of a line is

$\begin{gathered} y=mx+b \\ m\rightarrow\text{ slope} \\ b\rightarrow\text{ y-intercept} \end{gathered}$

Therefore, in our case,

$\begin{gathered} f(x)=x=1*x+0 \\ \Rightarrow slope=1,\text{ y-intercept}=0 \\ g(x)=3x-2 \\ \Rightarrow slope=3,\text{ y-intercept}=-2 \end{gathered}$

Thus, the slope of g(x) is greater than that of f(x), and g(x) is f(x) shifted 2 units down.

The answer is option C. g(x) is the steeper one, and the y-intercept has been shifted down.