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Standard Level

2.02 Power functions

Worksheet
Power functions
1

Do the following graphed functions have an even or odd power?

a
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
b
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
c
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
d
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
e
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
2

Consider the function y = x^{2}.

a

Complete the following table of values:

x- 3- 2- 10123
y
b

Using the points in the table, plot the curve on a cartesian plane.

c

Are the y-values ever negative?

d

Write down the equation of the axis of symmetry.

e

What is the minimum y-value?

f

For every y-value greater than 0, how many corresponding x values are there?

3

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

a

Does the graph rise or fall to the right?

b

Does the graph rise or fall to the left?

4

Consider the functions f(x) = - x^{4} and g(x) = - x^{6}.

a

Graph f(x) = - x^{4} and g(x) = - x^{6} on the same set of axes.

b

Which of the above functions has the narrowest graph?

5

Consider the functions f(x) = x^{3} and g(x) = x^{5}.

a

Graph f(x) = x^{3} and g(x) = x^{5}.

b

How would the graph of y = x^{7} differ to the graph of f(x) = x^{3} and g(x) = x^{5} ?

6

Consider the function y = x^{7}.

a

As x approaches infinity, what happens to the corresponding y-values?

b

As x approaches negative infinity, what happens to the corresponding y-values?

c

Sketch the general shape of y = x^{7}.

d

Sketch the general shape of y = - x^{7}.

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