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3.05 Transformations of functions

Interactive practice questions

This is a graph of $y=\frac{1}{x}$y=1x.

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A cartesian plane is shown with both the x-axis and y-axis ranging from -10 to 10. A hyperbola is plotted with a function $y=\frac{1}{x}$y=1x.
a

How do we shift the graph of $y=\frac{1}{x}$y=1x to get the graph of $y=\frac{1}{x}+3$y=1x+3?

Move the graph $3$3 units to the left.

A

Move the graph upwards by $3$3 unit(s).

B

Move the graph downwards by $3$3 unit(s).

C

Move the graph $3$3 units to the right.

D
b

Hence sketch $y=\frac{1}{x}+3$y=1x+3 on the same graph as $y=\frac{1}{x}$y=1x.

A cartesian plane is shown with both the x-axis and y-axis ranging from -10 to 10. A hyperbola is drawn with a function y = 1/x.
Loading Graph...
Easy
1min

A graph of $y=x^4$y=x4 is shown here. By dragging the points provided, plot the curve after it has undergone transformations resulting in the function $y=x^4-2$y=x42.

Easy
< 1min

How do we shift the graph of $y=f\left(x\right)$y=f(x) to get the graph of $y=f\left(x\right)+4$y=f(x)+4?

Easy
< 1min

How do we shift the graph of $y=g\left(x\right)$y=g(x) to get the graph of $y=g\left(x+6\right)$y=g(x+6)?

Easy
< 1min
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Outcomes

1.1.26

examine translations and the graphs of y=f(x)+a and y=f(x-b)

1.1.27

examine dilations and the graphs of y=c f(x) and y=f(dx)

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