Grade 11 · MCR3U · Functions

MCR3U Exponential Functions Practice Test (with Solutions)

Exponential Functions starts with exponent laws and ends with growth and interest problems. The free test is 8 multiple-choice questions: negative and rational exponents, transformations of y = 9ˣ and y = 8ˣ, a population model and an investment. Get the exponent laws automatic first, because everything else in the unit leans on them.

Free Exponential Functions Practice Test

8 questions, exactly as a free account gets them in the first Exponential Functions test on Martian Lab. Try each one on paper first, then open the answer.

Evaluate the expression $\dfrac{x^{-3}}{y^n}$ for $x = 4, y = 7, n = -2$ .
1. $\dfrac{49}{64}$
2. $\dfrac{64}{49}$
3. $\dfrac{7}{8}$
4. 3136
Show answer
a) $\dfrac{49}{64}$
Which of the following is equivalent to the expression $\left(a^3 b^4\right)^{-2}\!\left(a^{-3}b^{-5}\right)^{-4}$ ?
1. $a^6 b^{12}$
2. $a^{12}b^{15}$
3. $\dfrac{1}{a^6 b^{12}}$
4. $\dfrac{1}{a^6 b^7}$
Show answer
a) $a^6 b^{12}$
Which of the following is equivalent to the expression $\left(\dfrac{\sqrt[3]{z^7}}{\sqrt{z^5}}\right)^4$ ?
1. $\dfrac{1}{\sqrt{z^3}}$
2. $z$
3. $\sqrt[35]{z^4}$
4. $\dfrac{1}{\sqrt[3]{z^2}}$
Show answer
d) $\dfrac{1}{\sqrt[3]{z^2}}$
Which of the following functions represents $f(x) = 9^x$ after a reflection on the $x$ -axis and a vertical translation 5 units down?
1. $g(x) = -\!\left(9^{x-5}\right)$
2. $g(x) = 9^{-x+5}$
3. $g(x) = -\!\left(9^x\right) - 5$
4. $g(x) = -\!\left(9^x\right) + 5$
Show answer
c) $g(x) = -\!\left(9^x\right) - 5$
Which of the following is a transformation applied to the base function of $f(x) = 6\!\left(8^{-x-2}\right) - 4$ ?
1. A horizontal translation 2 units to the left.
2. A horizontal stretch by the factor 6.
3. A reflection on the $x$ -axis.
4. A vertical translation 2 units down.
Show answer
a) A horizontal translation 2 units to the left.
Which of the following functions represents $f(x) = 8^x$ after a vertical compression by the factor $\dfrac{1}{4}$ and a reflection on the $y$ -axis?
1. $g(x) = \dfrac{1}{4}\!\left(8^{-x}\right)$
2. $g(x) = -\dfrac{1}{4}\!\left(8^x\right)$
3. $g(x) = 8^{-\frac{1}{4}x}$
4. $g(x) = -\!\left(8^{4x}\right)$
Show answer
a) $g(x) = \dfrac{1}{4}\!\left(8^{-x}\right)$
The growth in population of a town since 2000 is given, in thousands, by the function $P(n) = 36.5(1.06)^n$ . In which year will the population expect to reach 70,000?
1. 2008
2. 2011
3. 2010
4. 2013
Show answer
b) 2011
In 1999, a sum of $600 is invested at a rate of 2.9% per year for 8 years. What is the value of the investment when it matures?
1. $739.20
2. $754.18
3. $1258.40
4. $3000
Show answer
b) $754.18

This Unit on Martian Lab

The lessons cover exponent laws, transformations of exponential functions, exponential equations and applications.

Exponent Laws
Transformations of Exponential Functions
Exponential Equations
Exponential Applications

Then 4 full Exponential Functions practice tests to check yourself.

Start Exponential Functions free

Exponential Functions FAQ

What is on an MCR3U exponential functions test?+

Exponent laws with negative and rational exponents, transformations of exponential functions, solving exponential equations, and growth and decay applications. The free questions on this page cover the laws, the transformations and the applications.

How do you deal with a negative exponent?+

Flip it: x⁻ⁿ = 1/xⁿ. So 4⁻³ / 7⁻² = 7² / 4³ = 49/64.

How do rational exponents work?+

The denominator is the root and the numerator is the power, so the cube root of z⁷ is z^(7/3). Turn every root into an exponent, use the exponent laws, then turn it back into a root if the answer asks for one.

How do you read the transformations of an exponential function?+

Write it as y = a·b^(k(x - d)) + c. In f(x) = 6(8^(-x - 2)) - 4 the exponent factors to -(x + 2): a reflection in the y-axis, a translation 2 units left, a vertical stretch by 6 and a translation 4 units down.

How do you work out compound interest?+

A = P(1 + i)ⁿ, with i the rate per period and n the number of periods. $600 at 2.9% a year for 8 years grows to 600(1.029)⁸ ≈ $754.18.

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