Unit 1-A Test – Polynomial and Rational Functions

State whether the graph to the right represents a function that is even, odd, or neither.

• The graph represents an even function.

• The graph represents an odd function.

• The graph represents neither an even nor an odd function.

• The graph represents a periodic function.

Tags

CCSS.HSF.BF.B.3

• The average rate of change is -0.125.

• The average rate of change is 0.125.

• The average rate of change is 0.25.

• The average rate of change is -0.25.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Find the degree of the polynomial from the given input and output values.

• The degree of the polynomial is 3.

• The degree of the polynomial is 2.

• The degree of the polynomial is 4.

• The degree of the polynomial is 1.

The values of the function are given as selected x-values in the table. The function's concavitiy does not change. Determine if the function is concave up or concave down. Justify your answer.

• The function is concave up because its second derivative is positive.

• The function is concave down because its second derivative is positive.

• The function is concave up because its first derivative is negative.

• The function is concave down because its second derivative is zero.

Using the information in the table, find the average rate of change on the interval 15 to 100 seconds.

• The average rate of change on the interval 15 to 100 seconds is ≈ 0.176 feet per second.

• The average rate of change on the interval 15 to 100 seconds is ≈ -0.176 feet per second.

• The average rate of change on the interval 15 to 100 seconds is ≈ 0.214 feet per second.

• The average rate of change on the interval 15 to 100 seconds is ≈ 0.167 feet per second.

Let the function f be increasing or decreasing, but not both. State whether the function is increasing or decreasing on the interval 12 < x < 16 and justify your answer.

• The function is decreasing on the interval 12 < x < 16 because for all a and b in the interval, if a < b, then f(a) > f(b).

• The function is increasing on the interval 12 < x < 16 because for all a and b in the interval, if a < b, then f(a) < f(b).

• The function is increasing on the interval 12 < x < 16 because for all a and b in the interval, if a > b, then f(a) > f(b).

• The function is decreasing on the interval 12 < x < 16 because for all a and b in the interval, if a < b, then f(a) < f(b).

• -8.998

• -9.125

• 8.990

• 9.125

Let f be a polynomial function with values f(0) = 3, f(8) = 0, and f(10) = 0. Are there any guaranteed extrema? If so, state where they occur.

• Yes, on the interval

  8 < x < 10.

• No, there are no guaranteed extrema because the function values at the endpoints are not equal.

• Yes, but only in the interval (0, 8) because f(0) ≠ f(8).

• No, because the function is not continuous on the interval (0, 10).

• The rate of change of the average rates of change is constant and equal to -10.

• The rate of change of the average rates of change is variable and depends on x.

• The rate of change of the average rates of change is zero for all x.

• The rate of change of the average rates of change is equal to 2 - 10x.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

The degree of a polynomial is 9 with real zeros at x = -4, x = 0, and x = 6. x = 0 has a multiplicity of 3. How many non-real zeros does the polynomial have?

• 2

• 4

• 6

• 8