Graphing Exponential and Logarithmic Functions

Presentation

•

Mathematics

•

9th - 12th Grade

•

Hard

Joseph Anderson

FREE Resource

16 Slides • 20 Questions

Page 172

Multiple Choice

Classify the following graph.

Exponential Growth

Exponential Decay

Logarithmic

Rational

The logarithmic function is the inverse function of the exponential function.

page172

Logarithmic Function

Domain

THE DOMAIN WILL ALWAYS BE -INFINITY TO +INFINITY

Multiple Choice

What is the domain?

(-∞, ∞)

(0, ∞)

[1, ∞)

(1, ∞)

Logarithm Functions

Include a VERTICAL asymptote

Multiple Choice

Where is the asymptote?

x = 1

y = 1

x = -1

y = -1

Multiple Choice

What is the x-intercept of log₇(x)?

(2, 0)

(-1, 0)

(0, 1)

(1, 0)

Multiple Choice

What is the range?

(-∞, ∞)

(0, ∞)

[1, ∞)

(1, ∞)

If b is...

Greater than 1 (b>1), the function is exponential GROWTH
Less than 1 and greater than 0 (0<b<1) the function is exponential DECAY

Definition of exponential function

Growth vs Decay

Multiple Choice

Is the pictured graph growth, decay, or linear or none?

Growth

Decay

Linear

None

Multiple Choice

Is the pictured graph growth, decay, or linear or none?

Growth

Decay

Linear

None

Basics of exponential functions. (page 2)

Multiple Choice

What is the domain of this function?

(-∞,0)

(-∞,∞)

(-∞,4)

(4,∞)

Multiple Choice

What is the domain of the function shown?

All real numbers

$y>0$

All real numbers greater than 1

$y<0$

Basics of exponential functions. (page 2)

Multiple Choice

What is the range of this function?

(-∞,0)

(0,∞)

(-∞,4)

(4,∞)

Range

Range is the y values of a function (up and down)
It is written lowest to highest
ONE of the values will be +/- inf.
What is the range of the graph?

Y- Intercept: one y-intercept

The y-intercept is "a"

y-intercept=1

X- Intercept: NO x-intercepts

PARENT FUNCTION ONLY

Key Features

Domain: all possible x values

D= all real numbers

Range: all possible y values

R= y>0

Asymptote: Imaginary line that the graph approaches, but never crosses

y=0

PARENT FUNCTION ONLY

Key Features

Transformations of Graphs

Multiple Choice

What is the range of the exponential function?

all real numbers

y > 3

y < 3

x > 3

Multiple Choice

What is the range of the exponential function?

all real numbers

y > -1

y < -1

x > -1

Transformations of Graphs

Multiple Choice

What is the y-intercept of the function?

-2

Exponential Functions

Include a HORIZONTAL asymptote

Multiple Choice

What is the equation of the horizontal asymptote for following exponential function?

y = -4

y > -4

y < -4

(0, -3)

Transformations?

Multiple Choice

Where would the asymptote be for this graph?

y = 4

y = -4

x = 3

x = -3

Multiple Choice

Which transformation is shown?

f(x)=2^x-1-3

f(x)=2^x-1+3

f(x)=2^x+1-3

f(x)=2^x+1+3

Multiple Choice

What is the domain of all exponential functions?

$\left(-\infty,\infty\right)$

$\left(0,\infty\right)$

$y>0$

$\left(-\infty,0\right)$

Multiple Choice

What transformation is the 2?

$y=3\left(\frac{1}{4}\right)^x+2$

stretch 2

shift up 2

reflection

grow 2

Multiple Choice

$y=4\left(\frac{1}{3}\right)^x-8$

What is the transformation of 4?

shrink 4

shift up 4

stretch 4

growth 4

Multiple Choice

$f\left(x\right)=-a\left(b\right)^x+k$

What causes a transformation of a reflection in the exponential formula?

the b

the a

the k

the negative in front of a

Page 172

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