Use shifts and scalings to transform the graph of $\text{ƒ}\left(x\right)=x^2$ into the graph of g. Use a graphing utility to check your work.


$g\left(x\right)=\text{ƒ}(2x-4)$

Area functions Let A(x) be the area of the region bounded by the t -axis and the graph of y=ƒ(t) from t=0 to t=x. Consider the following functions and graphs.

c. Find a formula for A(x)

ƒ(t) = {-2t+8 if t ≤ 3 ; 2 if t >3 <IMAGE>

Use shifts and scalings to transform the graph of $\text{ƒ}\left(x\right)=\sqrt{x}$  into the graph of g. Use a graphing utility to check your work.

$g\left(x\right)=3\sqrt{x-1}-5$

Area functions Let A(x) be the area of the region bounded by the t -axis and the graph of y=ƒ(t) from t=0 to t=x. Consider the following functions and graphs.

a. Find A(2) .

ƒ(t) = {-2t+8 if t ≤ 3 ; 2 if t >3 <IMAGE>

Shifting a graph Use a shift to explain how the graph of $\text{ƒ}\left(x\right)=\sqrt{-x^2+8x+9}$ is obtained from the graph of $g\left(x\right)=\sqrt{25-x^2}$ . Sketch a graph of ƒ.

Use shifts and scalings to transform the graph of $\text{ƒ}\left(x\right)=x^2$ into the graph of g. Use a graphing utility to check your work.

$g\left(x\right)=6\text{ƒ}\left(\frac{x-2}{3}\right)+1$

Use shifts and scalings to transform the graph of $\text{ƒ}\left(x\right)=\sqrt{x}$  into the graph of g. Use a graphing utility to check your work.

$g\left(x\right)=2\text{ƒ}(2x-1)$