Back to Tutor Intake Assessment: Graph polynomial functions

HSF.IF.C.7.c Tutor Intake — Polynomial Graphs: Zeros, End Behavior, Multiplicity

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Grade 9·12 problems·~14 min·Common Core Math - HS Functions·standard·hsf-if-c-7c

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Concepts

Which statement correctly describes the end behavior of
$f(x) = -3x^4 + 7x^2 - 2$ ?

Rises on the left, rises on the right

Falls on the left, falls on the right

Falls on the left, rises on the right

Rises on the left, falls on the right

Consider $f(x) = (x - 2)^2(x + 5)$ .
At $x = 2$ , how does the graph behave?

The graph crosses the x-axis

The graph touches (bounces off) the x-axis without crossing

The graph has a vertical asymptote

The graph has no x-intercept at $x = 2$

The polynomial $f(x) = x^3 + x^2 + x + 1$ has degree 3.
What is the maximum number of x-intercepts it can have?

Exactly 3

At most 3

Exactly 1

At most 2

A polynomial has degree 5. What is the maximum number of turning points
(local maxima and minima combined) its graph can have?

Procedures

What are the zeros of $f(x) = (x + 4)(x - 1)(x - 6)$ ?

$x = 4,\ x = -1,\ x = 6$

$x = -4,\ x = 1,\ x = 6$

$x = -4,\ x = 1,\ x = -6$

$x = 4,\ x = 1,\ x = 6$

Find the zeros of $g(x) = 3x^3 - 12x$ by factoring.
How many distinct real zeros does $g$ have?

What is the end behavior of $h(x) = 5x^3 - 2x^2 + 9x - 1$ ?

Rises on the left, rises on the right

Falls on the left, falls on the right

Falls on the left, rises on the right

Rises on the left, falls on the right

For $p(x) = (x + 3)^2(x - 1)^3(x - 5)$ , which of the following
correctly describes the graph behavior at each zero?

Bounces at $x = -3$ ; bounces at $x = 1$ ; crosses at $x = 5$

Crosses at $x = -3$ ; bounces at $x = 1$ ; crosses at $x = 5$

Bounces at $x = -3$ ; crosses at $x = 1$ ; crosses at $x = 5$

Crosses at $x = -3$ ; crosses at $x = 1$ ; bounces at $x = 5$

For $f(x) = -(x + 1)(x - 2)^2(x - 5)$ , what is the degree of $f$ ?

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