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Polynomials Graphs

This worksheet covers Polynomials Graphs, which is part of the Polynomials module in the SAT Math course. Practice problems are designed to strengthen key concepts and build confidence.

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Polynomial Operations

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Polynomials Graphs

Polynomials • SAT Math

Set 1 — Foundation

1.

What is the degree of the polynomial $p(x) = 3x^{4} - 5x^{2} + 2$ ?

A.

4

B.

2

C.

3

D.

1

2.

Which of the following is a polynomial function?

A.

$f(x) = x^{2} + 3x - 5$

B.

3.

What is the leading coefficient of the polynomial $p(x) = 2x^{3} - 4x^{2} + 5$ ?

4.

How many x-intercepts does the polynomial $p(x) = x^{2} - 4$ have?

A.

2

B.

1

C.

0

D.

3

5.

What is the y-intercept of the polynomial $p(x) = 4x + 7$ ?

A.

7

B.

4

C.

0

D.

11

6.

Which of the following polynomials has a negative leading coefficient?

A.

$f(x) = -3x^{2} + 4x - 1$

B.

7.

$Th$ e graph of which polynomial will be a parabola that opens upwards?

A.

$p(x) = x^{2} + 3$

B.

8.

What is the value of $p(-1)$ for the polynomial $p(x) = x^{3} - 2x + 1$ ?

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g(x) = \frac{1}{x} + 2

g (x) = \frac{1}{x} + 2

C.

$h(x) = \sqrt{x} + 4$

D.

$j(x) = e^x$

A.

2

B.

-4

C.

5

D.

3

$g(x) = 2x^{3} + x + 5$

C.

$h(x) = 0$

D.

$j(x) = 6x^{2} - 8$

$q(x) = -x^{2} + 2$

C.

$r(x) = -2x^{2} - 1$

D.

$s(x) = 3x^{2} - 4$

+

1

A.

2

B.

-2

C.

0

D.

1

9.

Which polynomial has a constant term of $5$ ?

A.

$f(x) = 3x^{2} + 5$

B.

$g(x) = 2x^{3} - x + 5$

C.

$h(x) = x^{2} - 4x$

D.

$j(x) = x^{2} + 3$

10.

What is the range of the polynomial $p(x) = -x^{2} + 4$ ?

A.

[ -\infty, 4 ]

B.

[ 4, \infty )

C.

[ -4, \infty )

D.

[ 4, -\infty )