Question

Families of functions Draw graphs of the given family of functions for c = 0.25, 0.5, 1, 2, 4. How are the graphs related?

$\mathit{f}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{=}{\mathbf{2}}^{\mathbf{c}\mathbf{x}}$.

Short answer

The graph is:

As c increased the graphs increased much faster.

Step-by-step solution

Step-1 – Given 

The given function is $f\left(x\right)=2^{cx}$.

Step-2 – To determine

We have to draw graphs of the given family of functions for c = 0.25, 0.5, 1, 2, 4. Then have to find a relation between them.

Step-3 – Calculation

For c = 0.25, we make a table for $f\left(x\right)=2^{cx}$.

$x$	–1	0	1
$f\left(x\right)$	0.840	1	1.1819

For c = 0.5, we make a table for $f\left(x\right)=2^{cx}$.

$x$	–1	0	1
$f\left(x\right)$	0.707	1	1.414

For c = 1, we make a table for $f\left(x\right)=2^{cx}$.

$x$	1	0	1
$f\left(x\right)$	0.5	1	2

For c = 2, we make a table for $f\left(x\right)=2^{cx}$.

$x$	–1	0	1
$f\left(x\right)$	0.25	1	4

For c = 4, we make a table for $f\left(x\right)=2^{cx}$.

$x$	-1	0	1
$f\left(x\right)$	0.0625	1	16

From the graph we see that, as c increased the graphs increased much faster.