Interactive practice questions
Consider the graph of $f\left(x\right)=x$f(x)=x below.
The function $f\left(x\right)$f(x) is transformed to give a new function $g\left(x\right)=f\left(x\right)+3$g(x)=f(x)+3.
Complete the table of values for the transformed function $g\left(x\right)$g(x).
| $x$x | $-1$−1 | $0$0 | $1$1 | $2$2 |
|---|---|---|---|---|
| $f\left(x\right)$f(x) | $-1$−1 | $0$0 | $1$1 | $2$2 |
| $g\left(x\right)$g(x) | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
The change that occurs by transforming $f\left(x\right)$f(x) to $g\left(x\right)$g(x) can be described as:
All function values increase by $3$3.
All function values decrease by $3$3.
Now draw the graph of $g\left(x\right)$g(x) on the same graph as $f\left(x\right)$f(x).
Consider the graph of $f\left(x\right)=4x$f(x)=4x given below.
The function $f\left(x\right)$f(x) is transformed to give a new function $g\left(x\right)=f\left(x-3\right)$g(x)=f(x−3).
Consider the graph of $f\left(x\right)$f(x) below.
The function $f\left(x\right)$f(x) is transformed to give a new function $g\left(x\right)=f\left(x\right)+3$g(x)=f(x)+3.
Consider the graph of $f\left(x\right)=3x^2$f(x)=3x2 below.
The function $f\left(x\right)$f(x) is transformed to give a new function $g\left(x\right)=f\left(x\right)+4$g(x)=f(x)+4.