Sample quiz on stretches and compressions of functions Main home here.
Let $f(x)$ be a function. For $a> 1$, the transformation $af(x)$ amounts to $\cdots$?
Let $f(x)$ be a function. For $0< a < 1$, the transformation $af(x)$ amounts to $\cdots$?
Let $f(x)$ be a function. For $0< k < 1$, the transformation $f(kx)$ amounts to $\cdots$?
Let $f(x)$ be a function. For $k > 1$, the transformation $f(kx)$ amounts to $\cdots$?
Let $f(x)=x^2$. Find the image of the point $(2,4)$ after the transformation $g(x)=5f(x)$.
Let $f(x)=\sqrt{x}$. Find the image of the point $(4,2)$ under the transformation $g(x)=f(2x)$.
Let $f(x)=\sqrt{x}$. Relative to $f(x)$, what transformation produces $g(x)=2\sqrt{x}$?
Let $f(x)=\sqrt{x}$. Relative to $f(x)$, what transformation produces $g(x)=\sqrt{2x}$?
Given $f(x)=\sqrt{x}$, one can obtain $g(x)=\sqrt{9x}$ via a horizontal compression (factor $k$) and separately via a vertical stretch (factor $a$). Find $k$ and $a$.
Let $f(x)=x^2$. Find a horizontal compression that will have the same effect as the vertical stretch $g(x)=4x^2$.
Describe the transformation needed to produce $g(x)=\frac{4}{x}$ from $f(x)=\frac{1}{x}$.
Describe the transformation needed to produce $g(x)=|5x|$ from $f(x)=|x|$.
What function results from stretching $f(x)=x^2$ vertically by a factor of $8$?
What function results from compressing $f(x)=|x|$ horizontally by a factor of $\frac{2}{3}$?
Let $f(x)=\sqrt{x}$. What is the domain of the new function $g(x)=\sqrt{10x}$?
Let $f(x)=\frac{1}{x}$. What is the domain of the transformed function $g(x)=\frac{1}{3x}$?
Let $f(x)=x^2$. After being horizontally compressed by $\frac{1}{2}$, then vertically stretched by a factor of $2$, the resulting function is $\cdots$?
Let $f(x)=\sqrt{x}$. Find the range of the transformed function $g(x)=\sqrt{4x}$.
Let $f(x)=|x|$. Find the image of the point $(-1,1)$ after the transformation $g(x)=2f(x)$.
Let $f(x)=\frac{1}{x}$. Find the image of the point $\left(\frac{1}{2},2\right)$ after the transformation $g(x)=f(\frac{1}{2}x)$.