Interactive practice questions
Consider the function $f\left(x\right)=-\frac{2}{x^2}$f(x)=−2x2.
How can the graph of $f\left(x\right)$f(x) be obtained from the graph of $y=\frac{1}{x^2}$y=1x2?
Vertical stretch by a factor of $2$2, reflection about the $y$y-axis.
Horizontal stretch by a factor of $2$2, reflection about the $y$y-axis.
Horizontal stretch by a factor of $2$2, reflection about the $x$x-axis.
Vertical stretch by a factor of $2$2, reflection about the $x$x-axis.
Which of these is the graph of $f\left(x\right)$f(x)?
What is the domain of $f\left(x\right)$f(x)? Give your answer in interval notation.
What is the range of $f\left(x\right)$f(x)? Give your answer in interval notation.
The function $f\left(x\right)=-\frac{3}{x^2}$f(x)=−3x2 is formed by reflecting $\frac{1}{x^2}$1x2 about the $x$x-axis and stretching it vertically.
Consider the function $f\left(x\right)=\frac{1}{\left(x-4\right)^2}$f(x)=1(x−4)2.
The function $f\left(x\right)=\frac{1}{\left(x-5\right)^2}$f(x)=1(x−5)2 can be represented by translating the graph of $\frac{1}{x^2}$1x2 horizontally.