Function Behavior From a Calculus Perspective

Determine the direction of

f(x) = -3x + 7.

• Increasing

• Decreasing

• Constant

• Increasing then decreasing

Tags

CCSS.HSF.IF.C.7

Determine the interval over which the function is increasing.

• (-$∞$, 1)

• (-$∞$, 5)

• (1, $∞$)

• (5, $∞$)

Tags

CCSS.HSA.REI.D.10

Determine the interval over which the function is decreasing.

• (-$∞$, -1.549) U (0.215, $∞$)

• (-1.549, 0.215)

• (-$∞$, 0.631) U (-2.133, $∞$)

• (-2.133, 0.631)

Tags

CCSS.HSA.REI.D.10

Describe the curvature of

f(x) = 2x² - 7x + 3

• Concave down

• Concave up

• Concave down then concave up

• Concave up then concave down

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which function has no concavity?

• Linear

• Quadratic

• Cubic

• All functions have concavity

Identify the inflection point(s) on the following graph.

• A

• B

• C

• A and C

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Determine the interval over which the function is concave up.

• (-$∞$, A)

• (-$∞$, B)

• (B, $∞$)

• (C, $∞$)

f(x) is increasing from (-$∞$, A) and decreasing from (A, $∞$).

What is true about f(x)?

***CHECK ALL THAT APPLY***

• f(x) is concave up

• f(x) is concave down

• f(x) has an inflection point

• f(x) has a maximum point

• f(x) has a minimum point

Which function(s) below are concave up?

***CHECK ALL THAT APPLY***

• f(x) = 2x + 7

• g(x) = -2x² + 5x - 3

• h(x) = 3^x

• k(x) = 4(x + 3)² - 2

• a(x) = 3(x + 1)(x - 5)

What is the correct end behavior of

f(x) = 3x² + 6x - 11 ?

***CHECK ALL THAT APPLY***

• As x decreases without bound, f(x) decreases without bound.

• As x decreases without bound, f(x) increases without bound.

• As x increases without bound, f(x) decreases without bound.

• As x increases without bound, f(x) increases without bound.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7