Topics
2. Non-linear relationships
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AustraliaNSW
Year 12

2.04 The exponential graph

Lesson
Worksheet
Practice
Worksheet
Graphs of exponential functions
1

State whether or not the following graphs show an exponential function:

a
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
b
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
c
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
d
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
e
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
f
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
g
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
h
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
2

For each of the following functions:

i

Complete the following table of values:

x-5-4-3-2-101234510
y
ii

State whether the function is an increasing or decreasing function.

iii

Describe the rate of change of the function.

iv

State the y-intercept of the curve.

a
y = 3^{x}
b
y = 3^{ - x }
3

Consider the graph of the equation y = 4^{x}:

a

Is each y-value of the function positive or negative?

b

State the value of y the graph approaches but does not reach.

c

State the equation and name of the horizontal line, which y = 4^{x} gets closer and closer to but never intersects.

-3
-2
-1
1
2
3
x
-1
1
2
3
4
5
y
4

Consider each of the given functions.

i

What number is the value of the function always greater than?

ii

How many x-intercepts does the graph of the function have?

a
y = 8^{x}
b
y = 9^{-x}
5

Consider each of the given functions.

i

Can the value of y ever be zero or negative? Explain your answer.

ii

As the values of x get larger and larger, what value does y approach?

iii

As the values of x get smaller and smaller, what value does y approach?

iv

Find the y-intercept of the curve.

v

How many x-intercepts does the curve have?

vi

Sketch the graph.

a
y = 6^{x}
b
y = 8^{ - x }
6

Consider the graphs of the two exponential functions A and B:

a

Describe the common features of the two graphs.

b

Describe the difference between the two graphs.

c

One of the graphs has equation y = 2^{x} and the other has equation y = 4^{x}

Which is the graph of y = 4^{x}?

-3
-2
-1
1
2
3
x
-1
1
2
3
4
5
y
7

Consider the functions y = 2^{x}, y = 3^{x} and y = 5^{x}.

a
Sketch the three functions on the same set of axes.
b

State whether each of the following statements is true or false:

i

None of the curves cross the x-axis.

ii

They all have the same y-intercept.

iii

All of the curves pass through the point \left(1, 2\right).

iv

All of the curves have a maximum value.

c

State the y-intercept of each curve.

8

Consider the functions y = 2^{-x}, y = 3^{-x} and y = 5^{-x}.

a
Sketch the three functions on the same set of axes.
b
State the y-intercept of each curve.
c

Describe the nature of these functions for large values of x.

9

Consider the graph of the following functions y = 3^{x} and y = 3^{ - x }.

a

State the coordinates of the point of intersection of the two curves.

b

Describe the behaviour of both functions for large values of x.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-2
-1
1
2
3
4
5
6
7
8
9
y
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Outcomes

MS2-12-1

uses detailed algebraic and graphical techniques to critically evaluate and construct arguments in a range of familiar and unfamiliar contexts

MS2-12-6

solves problems by representing the relationships between changing quantities in algebraic and graphical forms

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