Standard Level
5.06 Transformations of functions
Interactive practice questions
Consider the parabola $y=x^2-3$y=x2−3.
a
Complete the table of values.
| $x$x | $-2$−2 | $-1$−1 | $0$0 | $1$1 | $2$2 |
|---|---|---|---|---|---|
| $y$y | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
b
Use the graph of $y=x^2$y=x2 to sketch a graph of $y=x^2-3$y=x2−3.
Loading Graph...
c
What is the $y$y value of the $y$y-intercept of the graph $y=x^2-3$y=x2−3?
d
Adding a constant to the equation $y=x^2$y=x2 corresponds to which transformation of its graph?
Vertical shift
A
Steepening of the graph
B
Horizontal shift
C
Reflection about an axis
D
Easy
2min
A graph of $y=x^3$y=x3 is shown here. By dragging the points provided, plot the curve after it has undergone transformations resulting in the function $y=x^3-4$y=x3−4.
Easy
< 1min
This is a graph of $y=\frac{1}{x}$y=1x.
Easy
1min
Consider a graph of $y=3^x$y=3x.
Easy
1min
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