1.5 Transformation of functions  (Page 12/22)

Tabular representations for the functions $f,g,$ and $h$ are given below. Write $g(x)$ and $h(x)$ as transformations of $f(x).$

$f(x)=3x^4$

$g(x)=\sqrt{x}$

$h(x)=\frac{1}{x}+3x$

$f(x)={(x-2)}^2$

$g(x)=2x^4$

$h(x)=2x-x^3$

$g(x)=-f(x)$

$g(x)=f(-x)$

$g(x)=4f(x)$

$g(x)=6f(x)$

$g(x)=f(5x)$

$g(x)=f(2x)$

$g(x)=f\left(\frac{1}{3}x\right)$

$g(x)=f\left(\frac{1}{5}x\right)$

$g(x)=3f\left(-x\right)$

$g(x)=-f(3x)$

The graph of $f(x)=\left|x\right|$ is reflected over the $y$ - axis and horizontally compressed by a factor of $\frac{1}{4}$ .

The graph of $f(x)=\sqrt{x}$ is reflected over the $x$ -axis and horizontally stretched by a factor of 2.

The graph of $f(x)=\frac{1}{x^2}$ is vertically compressed by a factor of $\frac{1}{3},$ then shifted to the left 2 units and down 3 units.

The graph of $f(x)=\frac{1}{x}$ is vertically stretched by a factor of 8, then shifted to the right 4 units and up 2 units.

The graph of $f(x)=x^2$ is vertically compressed by a factor of $\frac{1}{2},$ then shifted to the right 5 units and up 1 unit.

The graph of $f(x)=x^2$ is horizontally stretched by a factor of 3, then shifted to the left 4 units and down 3 units.

$g(x)=4{(x+1)}^2-5$

$g(x)=5{(x+3)}^2-2$

$h(x)=-2|x-4|+3$

$k(x)=-3\sqrt{x}-1$

$m(x)=\frac{1}{2}{x}^3$

$n(x)=\frac{1}{3}|x-2|$

$p\left(x\right)={\left(\frac{1}{3}x\right)}^3-3$

$q\left(x\right)={\left(\frac{1}{4}x\right)}^3+1$

$a(x)=\sqrt{-x+4}$

$g(x)=f(x)-2$

$g(x)=-f(x)$

$g(x)=f(x+1)$

$g(x)=f(x-2)$