Algebra 2 — Semester B Practice

Question 1 of 10

NYS 7A-7IEasy Diagram

How many real zeros does the polynomial graph show?

A2 real zeros

B1 real zero

C3 real zeros

D4 real zeros

Explanation

Real zeros = where the curve crosses the x-axis. Three crossings shown.

Question 2 of 10

NYS 6M-6PEasy Diagram

Which graph corresponds to f(x) = 1/x?

AA V-shape

BA parabola opening up

CA line through the origin

DA two-branch hyperbola in quadrants I and III

Explanation

f(x) = 1/x has two branches: positive x → positive y (Q I), negative x → negative y (Q III), with asymptotes at the axes.

Question 3 of 10

NYS 8A-8CEasy Diagram

Which conic equation does this represent?

AHyperbola

BParabola

CCircle: x² + y² = r²

DEllipse: x²/a² + y²/b² = 1

Explanation

Oval shape stretched horizontally → ellipse with horizontal major axis.

Question 4 of 10

NYS 8A-8CEasy Diagram

Identify the conic.

ACircle

BEllipse

CHyperbola

DParabola

Explanation

Equal radii in all directions → a circle.

Question 5 of 10

NYS 5A-5CEasy Diagram

Which graph shows exponential growth?

ANeither

BBoth

CA — curve rising more steeply

DB — curve falling toward x-axis

Explanation

Growth: starts low, rises rapidly. A matches; B is decay.

Question 6 of 10

NYS 5A-5CEasy Diagram

Which graph shows exponential decay?

AB (curve falling toward x-axis)

BNeither

CA (curve rising)

DBoth

Explanation

Exponential decay: starts high, falls toward zero. Graph B matches; graph A is exponential growth.

Question 7 of 10

NYS 7A-7IEasy Diagram

Match the end behavior to a possible polynomial.

Af(x) = x⁴ − 2x²

Bf(x) = −x⁴ + 1

Cf(x) = x³ − 1

Df(x) = x

Explanation

Both ends → +∞ matches even degree with positive leading. f(x) = x⁴ − 2x² qualifies.

Question 8 of 10

NYS 5A-5CMedium Diagram

Which equation matches this exponential graph?

Ay = (1/2)ˣ (decay)

By = x²

Cy = log₂(x)

Dy = 2ˣ (growth)

Explanation

Curve approaches 0 as x → −∞ and grows rapidly as x increases → exponential growth.

Question 9 of 10

NYS 6M-6PEasy Diagram

For the function whose graph approaches the dashed lines, what type of function is this most likely?

ALinear function

BAbsolute value

CPolynomial

DRational function

Explanation

Both vertical and horizontal asymptotes are characteristic of rational functions where degrees of numerator and denominator are similar.

Question 10 of 10

NYS 7A-7IMedium Diagram

The graph shown most likely belongs to which polynomial?

AEven-degree polynomial

BA line

COdd-degree polynomial with positive leading coefficient

DOdd degree, negative leading coefficient

Explanation

Left end goes up (+∞), right end goes down (−∞). That signature is odd degree, negative leading coefficient.

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