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 𝑓(𝑥)=6 intersects the 𝑦-axis.

  • A(6,0)
  • B(1,0)
  • C(0,1)
  • D(0,6)

Q3:

Determine the function represented by the graph shown.

  • A𝑦=2
  • B𝑦=2
  • C𝑦=2
  • D𝑦=2

Q4:

The graph of the function 𝑓(𝑥)=𝑎 passes through the point (3,1). What is the value of 𝑎?

Q5:

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

  • A𝑁=200𝑒
  • B𝑁=200(4)
  • C𝑁=20012
  • D𝑁=20014
  • E𝑁=20012

Q6:

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

  • A𝑁=12012lnln
  • B𝑁=120(3)
  • C𝑁=12012lnln
  • D𝑁=12013
  • E𝑁=120𝑒ln

Q7:

Which of the following graphs represents the equation 𝑦=4(2)?

  • A
  • B
  • C
  • D

Q8:

Which of the following graphs represents the equation 𝑦=14?

  • A
  • B
  • C
  • D
  • E

Q9:

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

  • A𝑦=4(1+3)
  • B𝑦=4(1+3)
  • C𝑦=4(13)
  • D𝑦=4(1+3)
  • E𝑦=4(13)

Q10:

Which of the following graphs represents the equation 𝑦=23?

  • A
  • B
  • C
  • D
  • E

Q11:

Which of the following graphs represents the equation 𝑦=2(3)?

  • A
  • B
  • C
  • D
  • E

Q12:

Which of the following graphs represents the equation 𝑦=5332?

  • A
  • B
  • C
  • D
  • E

Q13:

Which of the following graphs represents the equation 𝑦=23(3)?

  • A
  • B
  • C
  • D
  • E

Q14:

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

  • A𝐴=504
  • B𝐴=506
  • C𝐴=502
  • D𝐴=508
  • E𝐴=5010

Q15:

Which of the following graphs represents the equation 𝑦=3?

  • A
  • B
  • C
  • D
  • E

Q16:

Which of the graphs is that of 𝑓(𝑥)=23?

  • AD
  • BA
  • CB
  • DC

Q17:

Complete the sentence: The graph of an exponential function 𝑓(𝑥)=𝑎 with 𝑎>0 and 𝑎1.

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

Q18:

Which of the graphs is that of 𝑓(𝑥)=4(12)?

  • AB
  • BC
  • CA
  • DD

Q19:

To get the graph of 𝑦=5 from the graph of 𝑦=2, we must .

  • Ascale by a factor of loglog(5)(2) in the horizontal direction.
  • Bscale by a factor of 52 in the horizontal direction.
  • Cscale by a factor of loglog(2)(5) in the vertical direction.
  • Dscale by a factor of loglog(2)(5) in the horizontal direction.
  • Escale by a factor of loglog(5)(2) in the vertical direction.

Q20:

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

Find the 𝑦-intercept in the shown graph.

As this graph represents an exponential function, every 𝑦-value is multiplied by 𝑏 when 𝑥 increases by Δ𝑥. Find 𝑏 for Δ𝑥=2.

Find the equation that describes the graph in the form 𝑦=𝑎𝑏.

  • A𝑦=0.53
  • B𝑦=0.53
  • C𝑦=0.53
  • D𝑦=0.52
  • E𝑦=0.53

Q21:

Which of the following graphs represents the equation 𝑦=34(2)?

  • 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 𝐸(𝑥)=𝑒 (dashed) against 𝑃(𝑥)=𝑥 (solid) below shows that even though 𝑒=1>0=0, this quickly reverses.

Indeed, at 𝑥=2, the power function is much larger, where 𝑃(2)=1,024 while 𝐸(2)7.39 and 𝑃(5)10 while 𝐸(5)148.

Which function is larger at 𝑥=10, the power function or the exponential function?

  • AExponential
  • BPower

The curves below show the graph of ln𝑥 which is the same as 10𝑥ln above that of ln𝑒 which simplifies to 𝑥.

What do the indicated points tell you about 𝑃(11) and 𝐸(11)?

  • A𝑃(11)=𝐸(11)
  • B𝑃(11)<𝐸(11)
  • C𝑃(11)>𝐸(11)

A fact about the natural logarithm function is that the slope of its tangent at (𝑥,𝑥)ln is just 1𝑥. For the constant multiple 𝐿(𝑥)=10𝑥ln, the tangent has slope 10𝑥 at (𝑥,10𝑥)ln. What is the slope of this tangent line at the point (20,𝐿(20))? What is the equation of the line?

  • ASlope =12, line: 𝑦=12𝑥10+(20)ln
  • BSlope =2, line: 𝑦=2𝑥10+10(20)ln
  • CSlope =12, line: 𝑦=12𝑥20+10(20)ln
  • DSlope =2, line: 𝑦=2𝑥20+10(20)ln
  • ESlope =12, line: 𝑦=12𝑥10+10(20)ln

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

  • A10(20)1020ln
  • B10(10)1013ln
  • C20(20)+2080ln
  • D10(10)+1033ln
  • E20(20)2040ln

By considering the convexity of 𝐿(𝑥), what can we conclude about 𝑃(40) and 𝐸(40).

  • A𝐸(40)<𝑃(40)
  • B𝐸(40)>𝑃(40)
  • C𝐸(40)>𝑃(40)
  • D𝐸(40)=𝑃(40)
  • E𝐸(40)<𝑃(40)

Use this method of finding the equation of a tangent with a slope of 12, to find an integer 𝑛 such that 𝑒>𝑛.

  • A𝑛=480
  • B𝑛=632
  • C𝑛=350
  • D𝑛=362
  • E𝑛=463

Use this method, but this time with a slope 14, to find an integer 𝑛 such that 𝑒>𝑛.

  • A𝑛=463
  • B𝑛=350
  • C𝑛=493
  • D𝑛=362
  • E𝑛=480

Q24:

Assuming 𝑎>1, which axis is the graph of the exponential function 𝑓(𝑥)=𝑎 asymptotic to?

  • AThe positive 𝑦-axis
  • BThe negative 𝑦-axis
  • CThe positive 𝑥-axis
  • DThe negative 𝑥-axis

Q25:

If 0<𝑎<1, for which values of 𝑥 does the exponential function 𝑎 satisfy 0<𝑎<1?

  • A𝑥(0,)
  • B𝑥(,0]
  • C𝑥(,1]
  • D𝑥(1,)

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.