# Worksheet: Graphs of Exponential Functions

In this worksheet, we will practice sketching and identifying the graphical transformations of exponential functions.

**Q4: **

The graph of the function passes through the point . What is the value of ?

**Q6: **

Which of the following expressions does NOT describe the shown graph?

- A
- B
- C
- D
- E

**Q7: **

Which of the following graphs represents the equation ?

- A
- B
- C
- D

**Q9: **

Which of the following could be the equation of the curve?

- A
- B
- C
- D
- E

**Q10: **

Which of the following graphs represents the equation ?

- A
- B
- C
- D
- E

**Q12: **

Which of the following graphs represents the equation ?

- A
- B
- C
- D
- E

**Q13: **

Which of the following graphs represents the equation ?

- A
- B
- C
- D
- E

**Q14: **

Among these expressions, which one does NOT describe the shown graph?

- A
- B
- C
- D
- E

**Q18: **

Which of the graphs is that of ?

- AB
- BC
- CA
- DD

**Q19: **

To get the graph of from the graph of , we must .

- Ascale by a factor of in the horizontal direction.
- Bscale by a factor of in the horizontal direction.
- Cscale by a factor of in the vertical direction.
- Dscale by a factor of in the horizontal direction.
- Escale by a factor of in the vertical direction.

**Q20: **

Observe the given graph, and then answer the following questions.

Find the -intercept in the shown graph.

As this graph represents an exponential function, every -value is multiplied by when increases by . Find for .

Find the equation that describes the graph in the form .

- A
- B
- C
- D
- E

**Q21: **

Which of the following graphs represents the equation ?

- A
- B
- C
- D

**Q22: **

Mason argues that just as two data points are enough to uniquely determine a linear function, so too is an exponential function uniquely determined by two points on its graph. Is this true?

- Ayes
- Bno

**Q23: **

A close-up of the graphs of (dashed) against (solid) below shows that even though , this quickly reverses.

Indeed, at , the power function is much larger, where while and while .

Which function is larger at , the power function or the exponential function?

- AExponential
- BPower

The curves below show the graph of which is the same as above that of which simplifies to .

What do the indicated points tell you about and ?

- A
- B
- C

A fact about the natural logarithm function is that the slope of its tangent at is just . For the constant multiple , the tangent has slope at . What is the slope of this tangent line at the point ? What is the equation of the line?

- ASlope , line:
- BSlope , line:
- CSlope , line:
- DSlope , line:
- ESlope , line:

Since that tangent had a slope less than 1, it is bound to meet at some point. What is the -coordinate of this point to the nearest integer?

- A
- B
- C
- D
- E

By considering the convexity of , what can we conclude about and .

- A
- B
- C
- D
- E

Use this method of finding the equation of a tangent with a slope of , to find an integer such that .

- A
- B
- C
- D
- E

Use this method, but this time with a slope , to find an integer such that .

- A
- B
- C
- D
- E

**Q24: **

Assuming , which axis is the graph of the exponential function asymptotic to?

- AThe positive -axis
- BThe negative -axis
- CThe positive -axis
- DThe negative -axis

**Q25: **

If , for which values of does the exponential function satisfy ?

- A
- B
- C
- D