# Worksheet: Graphs of Exponential Functions

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

Q1:

Which graph demonstrates exponential growth?

• A • B • C • D Q2:

Determine the point at which the graph of the function intersects the -axis.

• A
• B
• C
• D

Q3:

Determine the function represented by the graph shown. • A
• B
• C
• D

Q4:

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

Q5:

Which of the following expressions does NOT describe the shown graph? • A
• B
• C
• D
• E

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 Q8:

Which of the following graphs represents the equation ?

• A • B • C • D • E 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 Q11:

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

Q15:

Which of the following graphs represents the equation ?

• A • B • C • D • E Q16:

Which of the graphs is that of ? • BA
• CB
• DC

Q17:

Complete the sentence: The graph of an exponential function with and .

• Acontains the point (0, 1)
• Bhas a horizontal asymptote at
• Cusually has both positive and negative -values
• Dhas a domain of positive real numbers

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