Assignments

This series of exercises is about exponential functions and their graphs. We discuss the various aspects: what is an exponential function, how does the graph looks like and how can you make a sketch of the graph without using a graphing calculator. We also make a start with solving exponential equations if you want to calculate the intersection of two exponential functions.

Select a question by clicking on it.

1. Draw the graph of the function:

$y=3^x$

What is the formula of the asymptote?

2. Draw the graph of the function:

$y=2^x-2$

What is the formula of the asymptote?

3. Draw the graph of the function:

$y=2.3^x$

Calculate the intersection point with the $Y$ -axis and the equation of the asymptote.

4. Draw the graph of the function:

$y=(\displaystyle\frac{1}{3})^x$

What is the formula of the asymptote?

5. Draw the graph of the function:

$y=(\displaystyle\frac{1}{2})^{-x}+1$

What is the formula of the asymptote?

6. Draw the graph of the function:

$y=2^{-x+1}$

What is the formula of the asymptote?

7. Draw the graph of the function:

$y=-2^{2x-1}$

What is the formula of the asymptote?

8. Draw the graph of the function:

$y=2.3^{-x+1}+1$

What is the formula of the asymptote?

9. Draw the graphs of the functions:

$f: y=3^x$

$g: y=(\displaystyle\frac{1}{3})^{x-1}+2$

Calculate the intersection point of both graphs.

10. For which value(s) of $p$ do the graphs of the functions:

$f: y=2^x$

$g: y=-(\displaystyle\frac{1}{2})^x+p$

have only one point in common.

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