Transformations: 동영상 및 연습문제

Given the function $y=g\left(x\right)$, how would the graph of $y=g(x-3)$ differ from the original graph?

Given the function $y=g\left(x\right)$, how would the graph of $y=-5g\left(x\right)$ differ from the original graph?

Apply the transformations on the graph of $p\left(x\right)=x^2$ into the graph of $h\left(x\right)=p(3x-6).$ Check your work with the help of a graphing utility.

Given the function $y=g\left(x\right)$, how would the graph of $y=g\left(6x\right)$ differ from the original graph?

Apply the transformations on the graph of $p(x) = x^2$ into the graph of $h(x)=5p(\(\frac{x-4}{6}\))+3$. Check your work with the help of a graphing utility.

Apply the transformations on the graph of $p\left(x\right)=\sqrt{x}$ into the graph of $h\left(x\right)=4p(3x-2)$. Check your work with the help of a graphing calculator.

Apply the transformations on the graph of $p\left(x\right)=\sqrt{x}$ into the graph of $h\left(x\right)=4\sqrt{x-3}-6$. Check your work with the help of a graphing calculator.

Use a shift to explain how the graph of $h\left(x\right)=\sqrt{-x^2-6x+27}$ is obtained from the graph of $p\left(x\right)=\sqrt{36-x^2}$. Which of the following transformations applies? Draw the graph of h(x).

Given the graph of the function $g\left(x\right)$, plot the graph of $y=g(x+3)$.

Given the graph of the function $g\left(x\right)$, plot the graph of $y=g(x-3)+1$.

Graph the function $g\left(x\right)=-5x^2$ using shifts and scaling methods.

Graph the function $g\left(x\right)=-2x^2+8x-6$ using shifts and scaling methods.

Given the graph of the function $h\left(x\right)$, sketch the graph of the function $h(x+3)$.

Given the graph of the function $h\left(x\right)$, sketch the graph of the function $h\left(3(x-2)\right)$.

Consider the graph of the function $f\left(x\right)=x^2$. Which of the following equations represents the graph of $f\left(x\right)$ after it has been compressed vertically by a factor of $3$?

Consider the graph of the function $h\left(x\right)=2x^2-5$. Which of the following equations represents the graph of $h\left(x\right)$ after it has been stretched horizontally by a factor of $3$?

Given the function $y=f\left(x\right)$, which transformation describes the graph of $y=f(x+4)$?

Given the function $y=g\left(x\right)$, which transformation describes the graph of $y=g(3x+2_{})$?

Given the function $y=f\left(x\right)$, which transformation describes the graph of $y=f\left(\frac{x}{4}\right)-5$?

Graph the function $y=-\sqrt{\frac{x}{2}+4}$ by starting with the graph of $y=\sqrt{x}$ and applying appropriate transformations.

Write the new equation after shifting the graph of $y=x^2$ as shown in the figure.

Write the new equation after shifting the graph of $y=x^2$ as shown in the figure.

Write the new equation after shifting the given graph as stated below. Also, plot both graphs using the same rectangular coordinate system.

$y=27x^3$ Left $3$ units, Down $3$ units

Write the new equation after shifting the given graph as stated below. Also, plot both graphs using the same rectangular coordinate system.

$y=\sqrt{5x}$, Left $8$ units

Write the new equation after shifting the given graph as stated below. Also, plot both graphs using the same rectangular coordinate system.

$y=\frac{1}{3}(x-5)+2$ Down $2$ units, right $3$ units

For the given function, draw the graph.

$y=\mid x-21\mid$

For the given function, draw the graph. Note: Treat the function in its radical form.

$y=(x+9{)}^{\frac{2}{3}}$

For the given function, draw the graph.

$y=(x+5{)}^{\frac{3}{2}}+2$

For the given function, draw the graph.

$y = \(\frac{3}{x^2}\) + 5$

Graph the function $y=\frac{1}{3x}+2$ using transformations on the given graph of $y=\frac{1}{x}$.