Topics
6. Exponential & Logarithmic Functions
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United States of AmericaFL
Grade 912

6.01 Key features of exponential functions

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

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

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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
Easy
1min

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

Easy
2min

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

Easy
3min

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

Easy
< 1min
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Outcomes

MA.912.AR.5.7

Solve and graph mathematical and real-world problems that are modeled with exponential functions. Interpret key features and determine constraints in terms of the context.

MA.912.F.1.1

Given an equation or graph that defines a function, determine the function type. Given an input-output table, determine a function type that could represent it.

MA.912.F.1.7

Compare key features of two functions each represented algebraically, graphically, in tables or written descriptions.

MA.912.F.2.2

Identify the effect on the graph of a given function of two or more transformations defined by adding a real number to the x- or y- values or multiplying the x- or y- values by a real number.

MA.912.F.2.3

Given the graph or table of f(x) and the graph or table of f(x)+k,kf(x), f(kx) and f(x+k), state the type of transformation and find the value of the real number k.

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