Algebra 2 — Semester B Practice

Question 1 of 10

NYS 8A-8CEasy Diagram

Which conic equation does this represent?

ACircle: x² + y² = r²

BHyperbola

CEllipse: x²/a² + y²/b² = 1

DParabola

Explanation

Oval shape stretched horizontally → ellipse with horizontal major axis.

Question 2 of 10

NYS 7A-7IEasy Diagram

How many real zeros does the polynomial graph show?

A4 real zeros

B3 real zeros

C2 real zeros

D1 real zero

Explanation

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

Question 3 of 10

NYS 5A-5CMedium Diagram

Which equation matches this exponential graph?

Ay = 2ˣ (growth)

By = (1/2)ˣ (decay)

Cy = log₂(x)

Dy = x²

Explanation

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

Question 4 of 10

NYS 5A-5CEasy Diagram

Which graph shows exponential growth?

ABoth

BB — curve falling toward x-axis

CA — curve rising more steeply

DNeither

Explanation

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

Question 5 of 10

NYS 6M-6PEasy Diagram

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

AA V-shape

BA parabola opening up

CA two-branch hyperbola in quadrants I and III

DA line through the origin

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 6 of 10

NYS 7A-7IEasy Diagram

Match the end behavior to a possible polynomial.

Af(x) = x

Bf(x) = x⁴ − 2x²

Cf(x) = x³ − 1

Df(x) = −x⁴ + 1

Explanation

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

Question 7 of 10

NYS 8A-8CEasy Diagram

Identify the conic.

AHyperbola

BEllipse

CParabola

DCircle

Explanation

Equal radii in all directions → a circle.

Question 8 of 10

NYS 7A-7IMedium Diagram

The graph shown most likely belongs to which polynomial?

AOdd degree, negative leading coefficient

BEven-degree polynomial

CA line

DOdd-degree polynomial with positive leading coefficient

Explanation

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

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?

APolynomial

BLinear function

CRational function

DAbsolute value

Explanation

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

Question 10 of 10

NYS 5A-5CEasy Diagram

Which graph shows exponential decay?

AA (curve rising)

BNeither

CB (curve falling toward x-axis)

DBoth

Explanation

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

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