Topics
7. Inverse Functions and Logarithms
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United States of America
Grades 9-12

7.04 Exponential functions and the natural base e

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

Consider the graph of the equation $y=4^x$y=4x.

Loading Graph...
A plot of $y=4^x$y=4x on a Coordinate Plane is an upward-sloping curve that represents exponential growth. As x increases, the y values rise rapidly. The graph passes through the point (0, 1), since $4^0=1$40=1, and approaches the x-axis asymptotically from above as x decreases, but never touches the x-axis. The curve is smooth and continuous.
a

What can we say about the $y$y-value of every point on the graph?

The $y$y-value of most points of the graph is greater than $1$1.

A

The $y$y-value of every point on the graph is positive.

B

The $y$y-value of every point on the graph is an integer.

C

The $y$y-value of most points on the graph is positive, and the $y$y-value at one point is $0$0.

D
b

As the value of $x$x gets large in the negative direction, what do the values of $y$y approach but never quite reach?

$4$4

A

$-4$−4

B

$0$0

C
c

What do we call the horizontal line $y=0$y=0, which $y=4^x$y=4x gets closer and closer to but never intersects?

A horizontal asymptote of the curve.

A

An $x$x-intercept of the curve.

B

A $y$y-intercept of the curve.

C
Medium
1min

Consider the function $y=3^x$y=3x.

Medium
2min

Consider the function $y=3^{-x}$y=3−x.

Medium
3min

If the graph of $y=2^x$y=2x is moved down by $7$7 units, what is its new equation?

Medium
< 1min
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Outcomes

A.CED.A.1

Create equations and inequalities in one variable and use them to solve problems.

A.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

F.IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F.IF.C.7.E

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F.IF.C.8

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.IF.C.8.B

Use the properties of exponents to interpret expressions for exponential functions.

F.BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

F.LE.A.3

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

F.LE.B.5

Interpret the parameters in a linear or exponential function in terms of a context.

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