NC.M3.U2.F-IF.4 & 7; A-REI.11 Re-Test Lesson

Instructions:
Earn an 80% or higher on this lesson to be able to re-attempt the questions that you missed tied to this standard from our Unit 2 Test.

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NC.M3.F-IF.4; F-IF.7, & A-REI.11

Increasing & Decreasing Intervals of a Function

​Increasing Function: A function is increasing when its slope is positive. (i.e. the line is pointing up)

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Decreasing Function: A function is decreasing when its slope is negative​. (i.e. the line is pointing down)

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Interval: An interval is like a certain part of a graph. For example, if I want to look at just the parts of a graph from x = 0 to x = 3, then this would be an interval.​

​Visuals:

​Give the intervals the function is increasing and decreasing:

​Give the intervals the function is increasing and decreasing:

Multiple Choice

Is the function increasing or decreasing?

• Increasing

• Decreasing

• Both

• Not enough information to determine

Multiple Choice

What intervals is this function increasing?

• -2 to 2

• 0 to 1

• -1 to 1

• 0 to 2

Multiple Choice

What intervals is this function decreasing?

• -3 to 3

• 0 to 3

• 1 to 3

• 2-3 to 0

Multiple Choice

What intervals is this function increasing?

• 0 to 360

• 90 to 270

• 0 to 90 and 270 to 360

• 0 to 90 and 180 to 270

Multiple Choice

Leslie's car travels about 25 miles per gallon of gas. D(x) = 25x represents the # of miles based on x gallons of gas. Her car needs 14 gallons of gas to be full. What is a reasonable domain and range?

• 0 ≤ x ≤ 350

  0 < D(x) < 14

• x < 14

  D(x) ≤ 350

• x > 14

  D(x) > 350

• 0 ≤ x ≤ 14

  0 < D(x) < 350

Fill in the Blanks

Matthew is making an open-top box by cutting squares out of the corners of a piece of paper that is 11 inches wide and 17 inches long, and then folding up the sides. If the side lengths of his square cutouts are x inches, then the volume of the box is given by: $V\left(x\right)=x\left(11-2x\right)\left(17-2x\right)$

Matthew graphs this function along with the function $B\left(x\right)=140$

Based on the restricted domain $\left(0<x<5.5\right)$ , for which values of x is the Volume increasing? (use only whole numbers.)

Think Quadratics

​Concave up vs. Concave down

​Think Linear

​Positive slope vs. Negative slope

​Summary of End Behaviors

Multiple Choice

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even
• Leading Coefficient Positive
  Degree - Odd
• Leading Coefficient Negative
  Degree - Even
• Leading Coefficient Negative
  Degree - Odd

Multiple Choice

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even
• Leading Coefficient Positive
  Degree - Odd
• Leading Coefficient Negative
  Degree - Even
• Leading Coefficient Negative
  Degree - Odd

Multiple Choice

Determine the end behavior of the polynomial by identifying the degree and leading coefficient.

f(x) = 5x⁴ - x + 6

• UP-UP

• UP-DOWN

• DOWN-UP

• DOWN-DOWN

Multiple Choice

f(x) = -5x⁷

• UP and UP
• DOWN and DOWN
• UP and DOWN
• DOWN and UP

Multiple Choice

f(x) = 3x² + 5x - 9

• UP and UP
• DOWN and DOWN
• UP and DOWN
• DOWN and UP

Multiple Choice

Describe the end behavior of the graph.

• down, down

• down, up

• up, down

• up, up

Multiple Choice

f(x) = 4 + 3x - 6x⁷ + 3x⁴

• UP and UP
• DOWN and DOWN
• UP and DOWN
• DOWN and UP

Reasonable Domain is: 0 < x < 8

Reasonable Range is: 80 < y < 440

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​Reasonable Domain and Range
y = 80 + 45x

Multiple Choice

Gracie's service club is raising money by wrapping presents in the mall. The function f(x) = 3x describes the amount of money, in dollars, the club will earn for wrapping x presents. They only have enough wrapping paper to wrap 1000 presents. Which best represents the reasonable domain and range?

• 1000 ≤ x ≤ 0

  3000 < f(x) < 0

• x ≥ 1000

  f(x) > 3000

• 0 ≤ x ≤ 1000

  0 < f(x) < 3000

• x ≤ 3000

  f(x) <1000

Fill in the Blanks

Matthew is making an open-top box by cutting squares out of the corners of a piece of paper that is 11 inches wide and 17 inches long, and then folding up the sides. If the side lengths of his square cutouts are x inches, then the volume of the box is given by: $V\left(x\right)=x\left(11-2x\right)\left(17-2x\right)$

Matthew graphs this function along with the function $B\left(x\right)=140$

What is a reasonable domain for V(x) in this context?

Multiple Choice

Matthew is making an open-top box by cutting squares out of the corners of a piece of paper that is 11 inches wide and 17 inches long, and then folding up the sides. If the side lengths of his square cutouts are x inches, then the volume of the box is given by: $$V\left(x\right)=x\left(11-2x\right)\left(17-2x\right)$$

Matthew graphs this function along with the function $$B\left(x\right)=140$$ .

What do the points of intersection between V(x) & B(x), within the domain $$0<x<5.5$$ , represent in terms of the box?

• The sizes of cutouts that will produce a box with a volume of 140 cubic inches or higher.

• The sizes of cutouts that will produce a box with a volume of 2 cubic inches or higher.

• The sizes of cutouts that will produce a box with a volume of 140 cubic inches or lower.

• The sizes of cutouts that will produce a box with a volume of 2 cubic inches or lower.

Multiple Choice

What is the domain and range of the path of the golf ball?

• $$Domain:\ 0\le x\le230$$ $$Range:\ 0\le y\le36$$

• $$Domain:\ 0<x<230\$$ $$Range:\ 6\le y\le110$$

• $$Domain:\ 6\le x\le110$$ $$Range:\ 0\le y\le36$$

Fill in the Blanks

Matthew is making an open-top box by cutting squares out of the corners of a piece of paper that is 11 inches wide and 17 inches long, and then folding up the sides. If the side lengths of his square cutouts are x inches, then the volume of the box is given by: $V\left(x\right)=x\left(11-2x\right)\left(17-2x\right)$

Matthew graphs this function along with the function $B\left(x\right)=140$

Rounding to the nearest whole number, what value of x will give her a box with the greatest volume?

Multiple Choice

Noah writes an expression that gives the volume of an open-top box in cubic inches in terms of the length of x in inches of the cutout squares use to make it. The graph that Noah gets is given. What is a functional domain for this graph?

• $$-1<x<5$$

• $$x>0$$

• $$0<x<2.5$$

• $$0<x<3.5$$

Multiple Choice

Noah writes an expression that gives the volume of an open-top box in cubic inches in terms of the length of x in inches of the cutout squares use to make it. The graph that Noah gets is given. What is Noah's approximate maximum value??

• 0

• 10

• 4

• 15