6. Indices, Exponentials and Logs
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
$x\ge0$x≥0
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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