New Zealand
Level 8 - NCEA Level 3

Transformations of Rational Functions

Interactive practice questions

Consider the function $f\left(x\right)=-\frac{2}{x^2}$f(x)=2x2.

a

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.

A

Horizontal stretch by a factor of $2$2, reflection about the $y$y-axis.

B

Horizontal stretch by a factor of $2$2, reflection about the $x$x-axis.

C

Vertical stretch by a factor of $2$2, reflection about the $x$x-axis.

D

Vertical stretch by a factor of $2$2, reflection about the $y$y-axis.

A

Horizontal stretch by a factor of $2$2, reflection about the $y$y-axis.

B

Horizontal stretch by a factor of $2$2, reflection about the $x$x-axis.

C

Vertical stretch by a factor of $2$2, reflection about the $x$x-axis.

D
b

Which of these is the graph of $f\left(x\right)$f(x)?

A

B

C

D

A

B

C

D
c

What is the domain of $f\left(x\right)$f(x)? Give your answer in interval notation.

d

What is the range of $f\left(x\right)$f(x)? Give your answer in interval notation.

Easy
Approx 2 minutes

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(x4)2.

The function $f\left(x\right)=\frac{1}{\left(x-5\right)^2}$f(x)=1(x5)2 can be represented by translating the graph of $\frac{1}{x^2}$1x2 horizontally.

Outcomes

M8-7

Form and use trigonometric, polynomial, and other non-linear equations

91575

Apply trigonometric methods in solving problems