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Quizzes > High School Quizzes > Mathematics

Practice Quiz: Matching Exponential Graphs

Sharpen your skills solving exponential equations

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Paper art promoting a trivia quiz on matching exponential expressions for high school students.

Which of the following equations represents exponential growth?
y = 2^x
y = (1/2)^x
y = -2^x
y = 2^(-x)
The function y = 2^x has a base greater than 1, which means that as x increases, the value of y grows. Exponential growth is characterized by this rapid increase.
In the function y = a · b^x, what is the y-intercept when x = 0?
a
b
0
a · b
When x is 0, the equation becomes y = a · b^0, and since any nonzero number raised to the 0 power equals 1, y = a. This is the y-intercept of the function.
For the function y = 3^x, what is the base and what type of function is it?
Base 3; exponential growth
Base x; exponential decay
Base 3; exponential decay
Base 3; linear growth
The base of the exponential function is the number being raised to the power x. Since 3 > 1, the function exhibits exponential growth.
Which graph feature is typical of an exponential growth function?
It passes through (0, 1) and increases rapidly as x increases.
It passes through (0, 0) and increases slowly.
It passes through (1, 0) and decays as x increases.
It is symmetric about the y-axis.
An exponential growth graph of the form y = b^x (with no vertical scaling) always passes through (0, 1) because b^0 = 1. As x increases, the function grows rapidly.
For the function y = (1/2)^x, what happens to the value of y as x increases?
It decreases toward 0.
It increases exponentially.
It remains constant.
It oscillates.
When the base of an exponential function is between 0 and 1, as in (1/2)^x, the function exhibits exponential decay. This means that y approaches 0 as x increases.
Given the function y = 2^(x + 1), how is its graph shifted compared to y = 2^x?
The graph shifts left by 1.
The graph shifts right by 1.
The graph shifts upward by 1.
The graph shifts downward by 1.
Replacing x with (x + 1) in the exponent moves the graph horizontally. This results in a shift to the left by 1 unit.
Which description best fits the graph of y = 3 · 2^x?
The graph passes through (0, 3) and rises steeply.
The graph passes through (0, 3) and falls as x increases.
The graph passes through (1, 2) and rises steeply.
The graph passes through (3, 0) and remains constant.
For y = 3 · 2^x, when x is 0 the output is y = 3, indicating that the graph passes through (0, 3). Since the base 2 is greater than 1, the function grows rapidly as x increases.
Which of the following is an equivalent expression for 4^x?
2^(2x)
2^(x + 2)
2^x + 2^x
(2^x)^2 + 1
The expression 4^x can be rewritten as (2^2)^x, which simplifies to 2^(2x). This shows the equivalence between the two forms.
Which equation is equivalent to y = e^(2x)?
y = (e^2)^x
y = 2^(e · x)
y = e^(x/2)
y = (x^2)^e
Expressing e^(2x) as (e^2)^x is a valid transformation that shows the base raised to the power x. This form clearly separates the constant base from the variable exponent.
Identify the vertical shift in the function y = 5 · (1/3)^(x - 2) + 4.
4
-2
5
1/3
The +4 at the end of the function indicates that the entire graph is shifted upward by 4 units. This is the vertical translation applied to the function.
Which of the following represents an exponential decay function?
y = 7 · (0.5)^x
y = 7 · 2^x
y = -7 · (0.5)^x
y = 7 · (1.5)^x
In an exponential function, if the base is between 0 and 1 (as in 0.5), the function demonstrates decay. The function y = 7 · (0.5)^x decreases as x increases.
For the function y = 3 · 2^(x - 3), what is the horizontal shift relative to y = 3 · 2^x?
It shifts right by 3.
It shifts left by 3.
It shifts up by 3.
It shifts down by 3.
The replacement of x with (x - 3) in the exponent results in a horizontal translation to the right by 3 units.
Rewrite the exponential equation 2^x = 8 in logarithmic form to solve for x.
x = log₂ 8
x = 8 · log₂ 2
x = log₈ 2
x = 8 / log₂ 2
Converting 2^x = 8 to logarithmic form gives x = log₂ 8. Since 8 is 2 raised to the 3rd power, x evaluates to 3.
Simplify the expression: 2^(x + 2) divided by 2^x.
4
2x + 2
2^(2x)
2
By applying the law of exponents for division, subtract the exponents: (x + 2) - x = 2, so the expression simplifies to 2^2, which equals 4.
If f(x) = 2^x and g(x) = 2^(x + 4), what is the difference between their y-intercepts?
15
5
16
4
The y-intercept of f(x) is 2^0 = 1, and for g(x) it is 2^(0 + 4) = 16. The difference between 16 and 1 is 15.
Given f(x) = 3^x and g(x) = 3^(x + 2) + 1, describe the transformations that convert f(x) into g(x).
Horizontal shift left by 2 and vertical shift up by 1.
Horizontal shift right by 2 and vertical shift up by 1.
Horizontal shift left by 2 and vertical shift down by 1.
Horizontal shift right by 2 and vertical shift down by 1.
In g(x), the expression (x + 2) indicates a horizontal shift to the left by 2 units, while the +1 outside the exponential indicates a vertical shift upward by 1 unit. These combined transformations convert f(x) into g(x).
An exponential function of the form y = a · b^x passes through the points (2, 12) and (4, 48). What is the value of the base b?
2
4
6
8
Dividing the equations a · b^2 = 12 and a · b^4 = 48 gives b^2 = 4, so b = 2 (assuming b > 0).
How is the graph of y = 2^x transformed in the function y = -2^(x - 1) + 3?
It is reflected over the x-axis, shifted right by 1, and shifted upward by 3.
It is reflected over the y-axis, shifted left by 1, and shifted upward by 3.
It is reflected over the x-axis, shifted left by 1, and shifted downward by 3.
No transformation occurs.
The negative sign in front of 2^(x - 1) indicates a reflection over the x-axis. The (x - 1) shows a horizontal shift to the right by 1, and the +3 shifts the graph upward by 3.
Solve for x using logarithms: 5^(x - 1) = 125.
4
3
5
6
Since 125 can be expressed as 5^3, equate the exponents: x - 1 = 3, which yields x = 4. Logarithms confirm that x = log₅(125) + 1 = 3 + 1.
Which equation represents an exponential function that has been reflected over the y-axis?
y = 2^(-x)
y = -2^x
y = 2^x
y = 2^(-x) + 1
Reflecting an exponential function over the y-axis is accomplished by replacing x with -x in the expression. Here, y = 2^(-x) is the correct transformation.
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Study Outcomes

  1. Analyze exponential expressions and associate them with their corresponding graphs.
  2. Interpret the characteristics of exponential functions, including growth and decay patterns.
  3. Identify equivalent forms of exponential equations through algebraic manipulation.
  4. Apply matching strategies to correctly link exponential expressions to their graphs.

Matching Exponential Graphs Equations Cheat Sheet

  1. Master the standard form - Exponential functions come alive in the form f(x) = a · bx, where "a" is your launch pad and "b" decides if you're skyrocketing (b > 1) or gently drifting down (0 < b < 1). Think of "a" as your starting power level and "b" as the rate that sets the entire adventure in motion. Symbolab guide
  2. Spot the key graph features - The graph of f(x) = bx always zooms through the point (0, 1) and glides along a horizontal asymptote at y = 0, hinting it gets close to zero but never quite touches. This is like watching an endless race that never crosses the finish line! SparkNotes overview
  3. Play with transformations - When you see f(x) = a · b(x − h) + k, you're simply sliding your curve h units right (or left if h is negative) and lifting it k units up (or down if k is negative). These simple slides and lifts are your creative toolkit to sculpt any exponential shape. AIMSSEC transformations
  4. Match equations to graphs - Become a detective by spotting y‑intercepts, asymptotes, and whether the curve is booming upward or fading downward. Practice with varied examples until you can pair any mysterious equation with its perfect picture. Intellectual Math worksheet
  5. Decode negative exponents - Flipping f(x) = bx into f(x) = b−x mirrors the graph across the y‑axis, turning growth into smooth decay. Think of it as reversing time on your exponential journey! SparkNotes recap
  6. Explore real‑world magic - From bacterial population booms to radioactive decay slow‑downs, exponential functions power up real‑life stories. Examining these contexts makes the math jump off the page and into your world. Symbolab applications
  7. Dive into the natural exponential - Meet f(x) = ex, where "e" (≈2.718) fuels continuous growth in biology, finance and beyond. Its unique properties will turn you into a continuous‑growth guru! Symbolab on ex
  8. Solve with logs - To crack exponential equations, line up the bases and unleash logarithms to isolate x. It's like using a secret decoder ring to reveal hidden exponents! Lamar tutorial
  9. Tap interactive tools - Reinforce your skills with dynamic online platforms that let you drag, drop and tweak exponential curves until you feel unstoppable. Practice problems become playtime! IXL exercises
  10. Practice like a pro - Consistent rehearsal across varied examples cements your confidence and sharpens your intuition. Before you know it, exponential functions will feel like second nature! MathBits Notebook practice
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