Extrema and Increasing Decreasing Intervals

​1.3 More on Functions and Their Graphs

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Multiple Choice

What is the increasing interval on the function shown? #4

• $$\left(-\infty,\ \infty\right)$$

• $$\left(-\infty,\ 3\right)$$

• $$\left(3,\ \infty\right)$$

• $$\left(3,\ \infty\right]$$

Multiple Choice

Identify where the function is decreasing. #1

• x < 0

• x > 0

• x < -3 , x > 3

• -3 < x < 3

Multiple Choice

What is the decreasing interval on the function shown? #3

• $$\left(-\infty,\ 1\right)$$

• $$\left(-\infty,\ 2\right)$$

• $$\left(2,\ \infty\right)$$

• $$\left(1,\ \infty\right)$$

Multiple Select

What is the interval of increase and decrease in the following function. #2

• Decreasing from (5, 0) and (0, 2)

• Decreasing from (-5, -2) and (0, 2)

• Increasing from $$\left(2,\infty\right)$$

• Increasing from (2, 6)

• Increasing from (-2, 0) and $$\left(2,\infty\right)$$

Multiple Choice

What is the decreasing interval on the function shown? #8

• $$\left(-\infty,\ -3\right)$$

• $$\left(-\infty,\ -4\right)$$

• $$\left(-4,\ \infty\right)$$

• $$\left(-3,\ \infty\right)$$

Multiple Choice

Where does the function increase? #11

• $$\left(-\infty,\ \infty\right)$$

• $$\left(0,\ \infty\right)$$

• $$\left(-\infty,\ 0\right)$$

• This function does not increase.

Multiple Choice

Which open interval is the function increasing? #16

• $$\left(-\infty,0\right)$$  

• $$\left(0,2\right)$$  

• $$\left(2,\infty\right)$$  

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Multiple Choice

Which one of the following functions is even? #17

• f(x) = x⁴ + x³
• g(x) = x⁴ + x²
• h(x) = x⁵ + x³
• k(x) = x³ + x

Multiple Choice

Which one of the following functions is odd? #18

• f(x) = 3x⁴ - 4x³
• g(x) = 5x⁴ + 3x²
• h(x) = 6x⁵ - x³
• k(x) = x⁶ + 8x²

Multiple Choice

Point (1,4) is a(n)...#35

• Absolute Maximum

• Absolute Minimum

• Local Maximum

• Local Minimum

Multiple Choice

Identify the type of symmetry based on the graph: #19

i. symmetric with respect to the x-axis

ii. symmetric with respect to the y-axis

iii. symmetric with respect to the origin

• i only

• ii only

• iii only

• i, ii, and iii

Multiple Choice

Identify the type of symmetry based on the graph: #23

i. symmetric with respect to the x-axis

ii. symmetric with respect to the y-axis

iii. symmetric with respect to the origin

• i only

• ii only

• iii only

• i, ii, and iii

Multiple Choice

Use the symmetry tests to determine if the given function is odd, even, or neither:  $$f\left(x\right)=x^5+1$$  #25

• odd

• even

• neither

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Multiple Choice

What is the relative maximum? #28

• y = 36 at x = 0
• y = -6.55 at x= -2.55
• (-∞, ∞)
• None

Multiple Choice

How many extrema (maximums and minimums) are in the picture? #29

• 2
• 3
• 4
• 5

Multiple Choice

What are the zeros of the function? #30

• 4,1
• 3,1,-2,-5
• -3, -1, 2, 5
• -2,4

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Multiple Choice

What are the x-intercepts of  f(x)=(x - 10)(x + 10) #31

• 10
• (10 , 0) and (-10 , 0)
• (0, -10) and (0, 10)
• 0

Fill in the Blanks

Multiple Choice

Evaluate f(0). #40

• 0

• 19

• 9

• -19

Multiple Choice

Find f(-2). #41

• -3
• 6
• 8
• -6

Multiple Choice

What is the DOMAIN of the function? #44

• (-∞, +∞)
• (-∞, -1] U [3, +∞)
• [-1, +∞)
• (-1, 0] U (0, +∞)

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Multiple Choice

#50

• 2a

• 2a - h

• 2a + h

• 2h