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F30 – Unit 5 – Exponential and Logarithmic Functions Name: ____________________________Unit 5 – Practice Test Date: _____________________________
Unit 5 – Exponential and Logarithmic Functions - PRACTICE TEST
1. For the following exponential function: y = 0.8x
a) Sketch the function
b) Determine the x-intercept(s) and y-intercept(s)
c) Determine the domain and range
d) Determine the end behavior, and if it is increasing or decreasing
2. For the following logarithmic function: y = 32
log x
a) Sketch the function
b) Determine the x-intercept(s) and y-intercept(s)
c) Determine the domain and range
d) Determine the end behavior, and if it is increasing or decreasing
1 2 3 4 5 6 7 8 9 10 11 12 13 14–1–2–3–4–5–6 x
1
2
3
4
5
6
–1
–2
–3
–4
–5
–6
y
1 2 3 4 5 6 7 8 9 10 11 12 13 14–1–2–3–4–5–6 x
1
2
3
4
5
6
–1
–2
–3
–4
–5
–6
y
F30 – Unit 5 – Exponential and Logarithmic Functions Name: ____________________________Unit 5 – Practice Test Date: _____________________________
3. For the following logarithmic function: y = −2.5 ln xa) Sketch the function
b) Determine the x-intercept(s) and y-intercept(s)
c) Determine the domain and range
d) Determine the end behavior, and if it is increasing or decreasing
4. Which exponential function matches each graph below? Provide your reasoning. (3 marks)
i) y=0.5(34 )
x
iii) y=5 ( 34 )
x
ii) y=0.5(43 )
x
iv) y=5 ( 43 )
x
a) b)
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
__________ __________
1 2 3 4 5 6 7 8 9 10 11 12 13 14–1–2–3–4–5–6 x
1
2
3
4
5
6
–1
–2
–3
–4
–5
–6
y
F30 – Unit 5 – Exponential and Logarithmic Functions Name: ____________________________Unit 5 – Practice Test Date: _____________________________
5. THIS WILL BE A WORD PROBLEM. There will be questions that go with it in context to the question. Here is an equation similar to the word problem. y=150 (0.25)x
a) Solve for y when x = 2
b) Solve for x when y = 50 000.
6. This will be a word problem. Find the regression equation for the following exponential function. X 1 3 5 7 9Y 75 48 21 11 7
b) Use the equation to determine when y = 30
c) Use the equation to determine when x = 0
F30 – Unit 5 – Exponential and Logarithmic Functions Name: ____________________________Unit 5 – Practice Test Date: _____________________________
7. Which function matches each graph below? Provide your reasoning.
i) y=13
logx iii) y=3 logx
ii) y=13
lnx iv) y=3 lnx
a) b)
1 2 3 4 5 6 7 8 9 10 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
1 2 3 4 5 6 7 8 9 10 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
__________ __________
8. Which function matches each graph below? Provide your reasoning. (3 marks)
i) y=2 (3 ) x iii) y=5 lnx
ii y=0.5(12 )
x
iv) y=2logx
a) b)
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
1 2 3 4 5 6 7 8 9 10 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
__________ __________
F30 – Unit 5 – Exponential and Logarithmic Functions Name: ____________________________Unit 5 – Practice Test Date: _____________________________
9. THIS WILL BE A WORD PROBLEM. There will be questions that go with it in context to the question. Here is an equation similar to the word problem. y=−80391.60 log x
a) Use the question to determine y when x = 33
b) Use the question to determine x when y = -10 000
10. This will be a word problem. Determine the logarithmic regression to the nearest hundredth. X (Percent) 95 75 50 20 10Y (minutes) 25 39 52 152 175
b) Use your equation to estimate the time at which there will be only one quarter of x.
c) Use the equation to determine the original amount of x.
F30 – Unit 5 – Exponential and Logarithmic Functions Name: ____________________________Unit 5 – Practice Test Date: _____________________________
F30 – Unit 5 – Exponential and Logarithmic Functions Name: ____________________________Unit 5 – Practice Test Date: _____________________________
F30 – Unit 5 – Exponential and Logarithmic Functions Name: ____________________________Unit 5 – Practice Test Date: _____________________________
F30 – Unit 5 – Exponential and Logarithmic Functions Name: ____________________________Unit 5 – Practice Test Date: _____________________________
F30 – Unit 5 – Exponential and Logarithmic Functions Name: ____________________________Unit 5 – Practice Test Date: _____________________________
F30 – Unit 5 – Exponential and Logarithmic Functions Name: ____________________________Unit 5 – Practice Test Date: _____________________________
