Question

- Polynomial Functions -Find at least five ordered pairs for each function; then graph the function.

Answer 1

Answer: Finding the end behavior. To find the end behavior of a function, we can examine the leading term when the function is written in standard form.

Explanation:

Answer 2

1. f(x) = -x² + 4x + 1

when x = 1, then:

f(1) = - 1² + 4(1) + 1

(1, 4)

when x = 2, then:

f(2) = - 2² + 4(2) + 1

(2, 5)

when x = 3, then:

f(3) = - 3² + 4(3) + 1

(3, 4)

when x = 4, then:

f(4) = - 4² + 4(4) + 1

(4, 1)

when x = 5, then:

f(5) = - 5² + 4(5) + 1

(5, -4)

Graph:

2. f(x) = 2x² - 8x + 3

when x = 1, then:

f(1) = 2(1)² - 8(1) + 3

(1, -3)

when x = 2, then:

f(2) = 2(2)² - 8(2) + 3

(2, -5)

when x = 3, then:

f(3) = 2(3)² - 8(3) + 3

(3, -3)

when x = 4, then:

f(4) = 2(4)² - 8(4) + 3

(4, 3)

when x = 5, then:

f(5) = 2(5)² - 8(5) + 3

(5, 13)

Graph:

3. f(x) = -1/2 x² - 2x + 3

when x = 1, then:

f(1) = -1/2 (1)² - 2(1) + 3

(1, 0.5)

when x = -4, then:

f(-4) = -1/2 (-4)² - 2(-4) + 3

(-4, 3)

when x = 0, then:

f(0) = -1/2 (0)² - 2(0) + 3

(0, 3)

when x = -2, then:

f(-2) = -1/2 (-2)² - 2(-2) + 3

(-2, 5)

when x = -5, then:

f(-5) = -1/2 (-5)² - 2(-5) + 3

(-5, 0.5)

Graph: