Hong Kong
Stage 4 - Stage 5

# Transformations of Logarithmic graphs

## Interactive practice questions

Consider the functions:

$f\left(x\right)=\log_2x$f(x)=log2x, $g\left(x\right)=\log_2\left(x+6\right)$g(x)=log2(x+6), $h\left(x\right)=\log_2x+6$h(x)=log2x+6 and $p\left(x\right)=6\log_2x$p(x)=6log2x

a

Determine each of the function values for when $x=2$x=2.

 $f$f$\left(2\right)$(2) $=$= $\editable{}$ $g$g$\left(2\right)$(2) $=$= $\editable{}$ $h$h$\left(2\right)$(2) $=$= $\editable{}$ $p$p$\left(2\right)$(2) $=$= $\editable{}$
b

Which of the following is true for the relationship between the function $f\left(x\right)=\log_2x$f(x)=log2x and the transformation $g\left(x\right)=\log_2\left(x+6\right)$g(x)=log2(x+6)?

As $x$x becomes very large, the difference between the function values of $f\left(x\right)$f(x) and $g\left(x\right)$g(x) becomes very large.

A

As $x$x becomes very large, the difference between the function values of $f\left(x\right)$f(x) and $g\left(x\right)$g(x) stays the same.

B

As $x$x becomes very large, the difference between the function values of $f\left(x\right)$f(x) and $g\left(x\right)$g(x) becomes very small.

C
c

Which of the following is true for the relationship between the function $f\left(x\right)=\log_2x$f(x)=log2x and the transformation $h\left(x\right)=\log_2x+6$h(x)=log2x+6?

As $x$x becomes very large, the difference between the function values of $f\left(x\right)$f(x) and $h\left(x\right)$h(x) becomes very large.

A

As $x$x becomes very large, the difference between the function values of $f\left(x\right)$f(x) and $h\left(x\right)$h(x) stays the same.

B

As $x$x becomes very large, the difference between the function values of $f\left(x\right)$f(x) and $h\left(x\right)$h(x) becomes very small.

C
d

Which of the following is true for the relationship between the function $f\left(x\right)=\log_2x$f(x)=log2x and the transformation $p\left(x\right)=6\log_2x$p(x)=6log2x?

As $x$x becomes very large, the difference between the function values of $f\left(x\right)$f(x) and $p\left(x\right)$p(x) stays the same.

A

As $x$x becomes very large, the difference between the function values of $f\left(x\right)$f(x) and $p\left(x\right)$p(x) becomes very small.

B

As $x$x becomes very large, the difference between the function values of $f\left(x\right)$f(x) and $p\left(x\right)$p(x) becomes very large.

C
Easy
3min

The graph of $y=\log_4x$y=log4x has a vertical asymptote at $x=0$x=0. By considering the transformations that have taken place, state the equation of the asymptote of:

Hard
2min

Write a fully simplified equation for when the graph of $y=\log_4x$y=log4x is translated seven units downward, six units to the left, and then reflected across the $x$x-axis.

Hard
1min