Graph Analysis of Polynomial Functions

The graph of g is shown above, where -5 ≤ x ≤ 4. The graph of g has points of inflection at x = -1 and x = 1. On what intervals is the graph of g concave up?

k is increasing at a decreasing rate over the interval 2 < x < 4.

• True

• False

Tags

CCSS.HSF.IF.B.4

The graph of k is concave down over the interval -4 < x < 4.

• True

• False

k is positive and the rate of change of k is positive over the interval (4, 6).

• True

• False

Tags

CCSS.HSF.IF.B.4

The graph of the polynomial function g is shown above. Use the graph to solve the following. Write your answers in interval notation.

Find where 𝑔(𝑥) > 0.

Find where 𝑔(𝑥) ≤ 0.

For $ h(x) = 4x^3(x + 7)^2(x - 3) $, find all real zeros and indicate the multiplicity of each zero.

Tags

CCSS.HSF-IF.C.7C

The graph of $ f $ is shown above. Which of the following statements about $ f $ is correct?

• The function $ f $ is positive and increasing.

• The rate of change of $ f $ is positive and increasing.

• The function $ f $ is negative and increasing.

• The rate of change of $ f $ is negative and increasing.

Tags

CCSS.HSF.IF.B.4

The graph of \( g \) has zeros at \( x = -2.4048 \ldots, 2.0493 \ldots \).

Tags

CCSS.HSF-IF.C.7C

The absolute minimum value of \( h \) is \(-70.8456 \ldots\) at \( x = -6.5 = b \).

The graph of \( h \) has zeros at \( x = 2.3398 \ldots, 6.2071 \ldots \).