Graphing Exponential & logrithmic Functions Lesson Notes

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

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​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​

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​

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X- Intercept​​: NO x-intercepts

​PARENT FUNCTION ONLY

​Key Features

​

Domain: all possible x values

​

​D= all real numbers

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Range: all possible y values

​

R= y>0​

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

​

y=0​

​

​

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​PARENT FUNCTION ONLY

​Key Features

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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

• 3

• 1

• -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