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Standard level

4.01 Exponential functions

Interactive practice questions

Consider the function $y=3^x$y=3x.

a

Complete the table of values.

$x$x $-5$5 $-4$4 $-3$3 $-2$2 $-1$1 $0$0 $1$1 $2$2 $3$3 $5$5 $10$10
$y$y $\frac{1}{243}$1243 $\frac{1}{81}$181 $\frac{1}{27}$127 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

Is $y=3^x$y=3x an increasing function or a decreasing function?

Increasing

A

Decreasing

B
c

How would you describe the rate of increase of the function?

As $x$x increases, the function increases at a constant rate.

A

As $x$x increases, the function increases at a faster and faster rate.

B

As $x$x increases, the function increases at a slower and slower rate.

C
d

What is the domain of the function?

all real $x$x

A

$x\ge0$x0

B

$x<0$x<0

C

$x>0$x>0

D
e

What is the range of the function?

Easy
4min

Consider the expression $3^x$3x.

Easy
1min

Of the two functions $y=4^x$y=4x and $y=5^x$y=5x, which increases more rapidly for $x>0$x>0?

Easy
< 1min

Consider the function $y=9^x$y=9x.

Easy
< 1min
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