1. Warm Up #8 Evaluate the expression when x = –4 1. x2 + 5x
(-4)2 + 5(-4)
–3(-4)3 – 2(-4)2 + 10
16 – 20
192 – -4
170

2. Check your HW

5. Identify polynomial functions
EXAMPLE 1
Identify polynomial functions
Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient. Ask yourself – are the exponents all whole numbers??? Are the coefficients real.
h (x) = x4 – x2 + 3 1
Yes, in standard form, deg 4, type quartic, LC 1 4
f (x) = 5x2 + 3x –1 – x No

6. GUIDED PRACTICE
for Examples 1
Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.
g (x) = 7x – πx2
k (x) = x + 2x – 0.6x5
ANSWER
ANSWER
Yes, No
Deg: 2, type: quadratic, LC: π

7. Evaluate by direct substitution
EXAMPLE 2
Evaluate by direct substitution
Use direct substitution to evaluate 5. f (x) = 2x4 – 5x3 – 4x + 8 when x = 3.
f (x) = 2x4 – 5x3 – 4x + 8
Write original function.
f (3) = 2(3)4 – 5(3)3 – 4(3) + 8
Substitute 3 for x.
= 162 – 135 –
Evaluate powers and multiply.
= 23
Simplify

8. GUIDED PRACTICE
for Example 2
Use direct substitution to evaluate the polynomial function for the given value of x.
f (x) = x4 + 2x3 + 3x2 – 7; x = –2
f (x) = (-2)4 + 2(-2)3 + 3(-2)2 – 7
f (x) = 16 – – 7
f (x) = 5

10. EXAMPLE 3
Evaluate by synthetic substitution
Use synthetic substitution to evaluate f (x) from Example 2 when x = 3.
7. f (x) = 2x4 – 5x3 – 4x + 8
STEP 1
Write the coefficients of f (x) in order of descending exponents. Write the value at which f (x) is being evaluated to the left.
The last number is the answer f (3) = 23 9 15 6 3 2 1 3 5 23
STEP 2 Bring down the first coefficient(leading)
STEP 3 Multiply by the x-value and add to the
next coefficient – continue to the end

11. Example 4 (not on paper) )
Use synthetic substitution to evaluate the polynomial function for the given value of x.
f(x) = 5x3 + 3x2 – x + 7; x = 2 10 26 50 5 13 25 57
The answer is 57

12. GUIDED PRACTICE
for Examples 3 and 4
Use synthetic substitution to evaluate the polynomial function for the given value of x.
8. f (x) = x4 + 2x3 + 3x2 -7; x = -2
- 2 -6 12
The answer is 5 1 3 -6 5

14. Polynomial End Behavior Even Functions
Positive Leading Coefficient
Right: f(x) +∞ as x +∞
Left: f(x) +∞ as x -∞
Even Functions
Negative Leading Coefficient
Left: f(x) -∞ as x -∞
Right: f(x) -∞ as x +∞

15. Polynomial End Behavior Odd Functions
Positive Leading Coefficient
Left: f(x) -∞ as x -∞
Right: f(x) +∞ as x +∞
Odd Functions
Negative Leading Coefficient
Left: f(x) +∞ as x -∞
Right: f(x) -∞ as x +∞

16. EXAMPLE 4
Standardized Test Practice
The correct answer is D.
ANSWER

17. GUIDED PRACTICE
for Examples 3 and 4
Describe the degree and leading coefficient and end behavior of the polynomial function whose graph is shown.
ANSWER
degree: odd, leading
coefficient: negative
Left: f(x) +∞ as x -∞
Right: f(x) -∞ as x +∞

19. Graph the polynomial function.
GUIDED PRACTICE
for Examples 5 and 6
Graph the polynomial function.
2. f(x) = x4 – x3 – 4x2 + 4 x
f(x) -3 76 -2 12 -1 2 4 1 2 -4 3 22

20. Textbook Homework Classwork Pages 341 – 342 (3- 48) multiples of 3
Worksheet 5.2 and finish all in class
Textbook Homework
Pages 341 – 342 (3- 48) multiples of 3