Final Review Practice from Unit 1

1.  The graph of a function  is shown in the figure.  Which of the following best describes the behavior of the graph of from point A to point B?

• The graph of k is increasing and concave up.

• The graph of k is increasing and concave down

• The graph of k is decreasing and concave up.

• The graph of k is decreasing and concave down.

The function  is a polynomial with the following end behavior:

 

Which of the following could be an expression for ?

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The graph of function f has a hole at x =−1 and a vertical asymptote at x = 3 . Which of the following functions could be f ( x) ?

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The table above shows values for a function f at selected values of x . Which of the following statements about f best fits these data?

• f is best modeled by a linear function because the rate of change over consecutive equal length input-value intervals is constant.

• f is best modeled by a linear function because the change in the average rates of change over consecutive equal-length input-value intervals is constant.

• f is best modeled by a quadratic function because the rate of change over consecutive equallength input-value intervals is constant

• f is best modeled by a quadratic function because the rate of change over consecutive equal-length input-value intervals is linear.

The polynomial function p is given by the function on the left. Which of the following could be the graph of p ?

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The rational function  is given by r.  Which of the following statements about  is correct?

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The table above shows values for the polynomial function g at selected values of x . Which of the following claim and explanation statements could be true about g ?

• The least possible degree of g is two.

• The least possible degree of

  g

  is three.

• The least possible degree of g is four.

• The least possible degree of g is five.

The functions m and n are defined for all real numbers. In the xy-plane , the graph of n is constructed by applying three transformations to the graph of m in this order: a horizontal dilation by a factor of 2 , a horizontal translation of 4 units, and a vertical translation of −8 units. Which of the following is the correct transformation that maps the graph of m to n in the same xy-plane ?

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The graph of f is shown above with the six points A, B, C, D, E, and F labeled. What are all the points where the graph of f has a local maximum?

• C only

• E only

• C and E only

• A, C, and E