Remediation 3.2 CFA Exponential Graphs

f(x)=ab^x

Growth and Decay

Multiple Choice

Is this function growth or decay?

• Growth

• Decay

Multiple Choice

Is this function growth or decay?

• Growth

• Decay

Multiple Choice

$$f\left(x\right)=\left(\frac{1}{2}\right)^x$$  Is this function growth or decay?

• Growth

• Decay

Multiple Choice

Which equation is considered a growth?

• $$f\left(x\right)=\left(\frac{1}{2}\right)^x-7$$

• $$f\left(x\right)=\left(0.98\right)^x+2$$

• $$f\left(x\right)=\left(1.67\right)^x+5$$

• $$f\left(x\right)=\left(.001\right)^x-1$$

Multiple Choice

How do you know that this was exponential growth? $$f\left(x\right)=0\ .25\ \left(\ 1.3\right)^x$$  

• Because the 0.25 was bigger than one

• Because the 1.3 was bigger than one

• Because the 0.25 was less than one

• Because the 1.3 was less than one

Transformations

• negative a = flip (reflect)

• opposite of h = right and left

• k = up and down

horizontal shifts

Vertical shift

Reflections

Multiple Select

What trnasformations are happening to the exponential function?

• up 1

• right 2

• right 3

• down 2

• left 2

Multiple Choice

The red and blue lines are reflected over which axis?

• y-axis

• x-axis

Multiple Choice

Which equation has an asymptote of -3?

• $$f\left(x\right)=\left(3\right)^x-9$$

• $$f\left(x\right)=\left(\frac{1}{2}\right)^x$$

• $$f\left(x\right)=-\left(3\right)^x$$

• $$f\left(x\right)=\left(2.5\right)^x-3$$

Multiple Choice

What transformations have happened to f(x) = 2^x if the new equation is
 g(x) = -2^(x+3) -6

• It stayed the same
• reflects, up 3, left 6
• reflects, right 3, down 6
• reflects, left 3, down 6

Multiple Choice

Asymptote?

• y = 2
• y = -2
• x = 2
• y = 0

Multiple Choice

The graph of $$y=3^x$$ is translated 7 units to the left and then 4 units upwards. What is the equation of the graph in its final position?

• $$y=3^{x-7}-4$$

• $$y=3^{x-7}+4$$

• $$y=3^{x+7}-4$$

• $$y=3^{x+7}+4$$

Multiple Choice

Which of the following describes the transformation of  $$f\left(x\right)=\frac{1}{2}\cdot2^{\left(x+2\right)}-3$$  from the parent graph  $$g\left(x\right)=2^x$$  

• Vertically shift down 3, horizontally shift left 2, and vertically compressed 1/2 units

• Vertically shift up 3, horizontally shift left 2, and vertically compressed 1/2 units

• Vertically shift down 3, horizontally shift right 2, and vertically compressed 1/2 units

• Vertically shift up 3, horizontally shift right2, and vertically compressed 1/2 units

Multiple Choice

What is the domain and range of the function y=2^x ?

Use the graph to help!

• Domain: $$\left(-\infty,\infty\right)$$

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

• Domain: $$\left(-\infty,\infty\right)$$

  Range: $$\left(1,\infty\right)$$

• Domain: $$\left[-2,\infty\right)$$

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

• Domain: $$\left(-\infty,\infty\right)$$

  Range: $$\left[0,\infty\right)$$

Multiple Choice

Range?

• (-8, ∞)
• [-8, ∞)
• (-∞, ∞)
• (∞, -8)

Multiple Choice

Range?

• (-∞, 2)
• (-∞, 2]
• (2, ∞)
• (2, -∞)

Multiple Choice

What is the domain of the function
y = -6^{x + 3} - 9

• (-∞, ∞)
• (-∞, -9)
• (-9, ∞)
• (∞, -∞)

Exponential Functions

f(x) = a (b)^x

^{a = initial value or starting amount}

^{b= (common ratio) growth or decay factor}

Multiple Choice

What is the initial value in y=4(2)^x

• 4

• 2

• x

Multiple Choice

What is the y-intercept in y=4(2)^x

• (4,0)

• (0,2)

• x

• (0,4)

• (4,2)

Multiple Choice

What is the y-intercept?

• (0,0)
• (0,1)
• (-3,0)
• (0,-3)

HA = 0

y intercept = 1

As the x's go up by 1

the y's go down by a factor of 1/2

f(x) = (1/2)^x

HA = 0

y intercept = 1

as x's increase by 1, the y's increase by a factor of 2

y = 2^x

Multiple Choice

What is the function for the graph?

• $$y=\frac{1}{3}\left(2\right)^x$$

• $$y=\left(\frac{1}{3}\right)^x$$

• $$y=\left(3\right)^x$$

• $$y=\left(3\right)^{\frac{1}{3}x}$$

Multiple Choice

What is the graph of the function 

$$y=5\cdot2^x$$  

Multiple Choice

Which exponential equation could represent the graph shown?

• $$f\left(x\right)=3^x+2$$

• $$f\left(x\right)=3^x-2$$

• $$f\left(x\right)=3^{\left(x+2\right)}$$

• $$f\left(x\right)=3^{\left(x-2\right)}$$

Multiple Choice

Which graph matches the equation?

Multiple Choice

How do you know that this was exponential decay? $$f\left(x\right)=\ 25\ \left(\ 0.20\right)^x$$  

• Because the 25 was bigger than one

• Because the 0.20 was bigger than one

• Because the 25 was less than one

• Because the 0.20 was less than one