Exponential Functions Test
[21 marks]
1
1. Which of the following is equivalent to 86 ?
a. (−8)6
b.
c.
1
86
6
8
6
d. √8
2. Which of the following is equivalent to 1?
a. 5−4 × 54
b. (−1)3
c.
134
13−4
3
d. 1 + 12
3. Which of the following is equivalent to 643?
a. 262 144
b. 16
c. 8
d. 4
2
4. Evaluate
273
1
−
27 3
a. 9
b. 3
c. 729
d. 27
5. Which of the following is equivalent to the expression (𝑎3 𝑏 4 )(𝑎−3 𝑏−5 )−4
a. 𝑎12 𝑏15
b.
c.
1
𝑎 6 𝑏12
1
𝑎6 𝑏7
6 12
d. 𝑎 𝑏
6. Which of the following functions represents 𝑓(𝑥) = 9𝑥 after a reflection on the x-axis and a
vertical transformation 5 units down?
a. 𝑔(𝑥) = 9−𝑥+5
b. 𝑔(𝑥) = −(9𝑥 ) − 5
c. 𝑔(𝑥) = −(9𝑥 ) + 5
d. 𝑔(𝑥) = −(9𝑥−5 )
7. What is the equation for the asymptote for the function 𝑓(𝑥) = 0.5(4𝑥−2 ) + 3
a. 𝑥 = 3
b. 𝑦 = −3
c. 𝑦 = 3
d. 𝑦 = 4
8. What are the domain and range of the function 𝑓(𝑥) = 4(2−2𝑥+3 ) − 7?
a. Domain ={𝑥 ∈ ℝ}
Range = {𝑦 ∈ ℝ|𝑦 < −7}
b. Domain = {𝑥 ∈ ℝ|𝑥 > 7}
Range = {𝑦 ∈ ℝ}
c. Domain ={𝑥 ∈ ℝ}
Range = {𝑦 ∈ ℝ}
d. Domain ={𝑥 ∈ ℝ}
Range = {𝑦 ∈ ℝ|𝑦 > −7}
9. Which of the following functions represents 𝑓(𝑥) = 8𝑥 after a vertical compression by the
factor ¼ and a reflection on the y-axis?
1
a. 𝑔(𝑥) = 8−4𝑥
b. 𝑔(𝑥) = −(84𝑥 )
1
c. 𝑔(𝑥) = 4 (8−𝑥 )
1
d. 𝑔(𝑥) = − 4 (8𝑥 )
10. Which function describes exponential decay?
a. 𝑓(𝑥) = 3.4(40)2𝑥
b. 𝑓(𝑥) = 25(0.8)𝑥
𝑥
c. 𝑓(𝑥) = 8(17)4
d. 𝑓(𝑥) = 6(1.01)𝑥
11. A bucket initially contains 425 mL of water. The volume of water in the bucket increases 4.8%
each hour. Which equation models the situation?
a. 𝑉(𝑡) = 425(4.8)𝑡
b. 𝑉(𝑡) = 425(0.952)𝑡
c. 𝑉(𝑡) = 425(0.048)𝑡
d. 𝑉(𝑡) = 425(1.048)𝑡
12. If you are looking at a table of values describe how you can use
first differences to determine if a function is exponential.
[2 marks]
13. What is the equation of the exponential function shown in the
graph to the right?
[2 marks]
14. Write the equation of an exponential function with an asymptote
at y = -7 and a y-intercept at 9.
[3 marks]
15. When a cast iron pan is placed in a hot oven its temperature
increases according to the equation below. [3 marks]
𝑇(𝑡) = −430(0.7𝑡 ) + 500
a. What is the initial temperature of the pan?
b. What is the temperature of the oven that the pan
approaches?
c. How would the heating of the pan change if the 0.7 in the
equation was changed to 0.9?