F30 – Unit 4 – Polynomial Functions Name: _________________Unit Practice Test Date: __________________

Unit 4 – Polynomial Functions – PRACTICE TEST1. Determine the following characteristics of the polynomial function f(x) = -x3 + 2x2 – x + 1. (7 marks)a) Degree, Shape and Leading Coefficient

b) number of possible x-intercepts

c) y-intercept

d) end behavior

e) domain

f) range

g) number of possible turning points

2. Determine the following characteristics of the polynomial function f(x) = 2(2x – 3)(x – 5)a) Degree, Shape, and Leading Coefficient

b) number of possible x-intercepts

c) x-intercept(s)

d) y-intercept

e) end behavior

f) vertex

g) domain

g) range

h) number of possible turning points

F30 – Unit 4 – Polynomial Functions Name: _________________Unit Practice Test Date: __________________

3. Write an equation for the following quadratic in general form

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

4. Write an equation for the following line in general form

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

5. For the following graph determine the leading coefficient and y-intercept and end behavior of the following cubic. On the test you will need to do this and match it to an equation.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

F30 – Unit 4 – Polynomial Functions Name: _________________Unit Practice Test Date: __________________

6. Write an equation for a polynomial function that satisfies each set of characteristics. Explain your reasoning.a) two turning points, positive function, y-intercept of 5

b) one turning point, has a minimum, y-intercept of 6

7. Plot the following graph

x 4 10 18 24 29 34 36 42y 1.5 2 1 3.5 4 3 2.5 3.5

a) Create a scatter plot, and draw a line of best fit for the data. (3 marks)

b) Write an equation for your line of best fit

c) Use your graph and equation to estimate the value of y when x is 48.

5

4

3

2

1

4 8 12 16 20 24 28 32 36 40 44 48-1

-2

-3

-4

F30 – Unit 4 – Polynomial Functions Name: _________________Unit Practice Test Date: __________________

8. Use the formula to find the equation of the linear regression.x 0 8 23 31 36 39 45 48 49y 10 9.95 9.93 9.86 9.84 9.79 9.77 9.72 9.58

a) Determine the equation of the linear regression function. (5 marks)

a=n¿¿

b) estimate x = 47

9. Regression function: f(n) = 0.0123 n3 – 0.4645n2 +6.295n + 23.452Estimate when n = 5

10. Find the cubic regression

X 999.87 999.75 1000.01 1001.44 1002.52 1000.59 1003.76Y 0 5 10 20 25 15 30

11. Find the Quadratic RegressionX 1 2 7 8 12 13 18 19 20 24 25Y 3.9 3.5 3.1 3.1 3.8 3.9 5.0 5.3 5.4 6.3 6.4

x y xy x2

F30 – Unit 4 – Polynomial Functions Name: _________________Unit Practice Test Date: __________________

F30 – Unit 4 – Polynomial Functions Name: _________________Unit Practice Test Date: __________________

F30 – Unit 4 – Polynomial Functions Name: _________________Unit Practice Test Date: __________________

F30 – Unit 4 – Polynomial Functions Name: _________________Unit Practice Test Date: __________________