Algebra 2 — Semester B Practice

Question 1 of 10

NYS 6M-6PEasy Diagram

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

AAbsolute value

BRational function

CLinear function

DPolynomial

Explanation

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

Question 2 of 10

NYS 7A-7IEasy Diagram

Match the end behavior to a possible polynomial.

Af(x) = x⁴ − 2x²

Bf(x) = x³ − 1

Cf(x) = x

Df(x) = −x⁴ + 1

Explanation

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

Question 3 of 10

NYS 7A-7IEasy Diagram

How many real zeros does the polynomial graph show?

A3 real zeros

B2 real zeros

C4 real zeros

D1 real zero

Explanation

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

Question 4 of 10

NYS 5A-5CMedium Diagram

Which equation matches this exponential graph?

Ay = 2ˣ (growth)

By = (1/2)ˣ (decay)

Cy = x²

Dy = log₂(x)

Explanation

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

Question 5 of 10

NYS 8A-8CEasy Diagram

Identify the conic.

ACircle

BHyperbola

CEllipse

DParabola

Explanation

Equal radii in all directions → a circle.

Question 6 of 10

NYS 8A-8CEasy Diagram

Which conic equation does this represent?

ACircle: x² + y² = r²

BEllipse: x²/a² + y²/b² = 1

CParabola

DHyperbola

Explanation

Oval shape stretched horizontally → ellipse with horizontal major axis.

Question 7 of 10

NYS 5A-5CEasy Diagram

Which graph shows exponential growth?

AA — curve rising more steeply

BB — curve falling toward x-axis

CNeither

DBoth

Explanation

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

Question 8 of 10

NYS 6M-6PEasy Diagram

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

AA V-shape

BA two-branch hyperbola in quadrants I and III

CA parabola opening up

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 9 of 10

NYS 7A-7IMedium Diagram

The graph shown most likely belongs to which polynomial?

AOdd degree, negative leading coefficient

BA line

COdd-degree polynomial with positive leading coefficient

DEven-degree polynomial

Explanation

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

Question 10 of 10

NYS 5A-5CEasy Diagram

Which graph shows exponential decay?

ANeither

BB (curve falling toward x-axis)

CA (curve rising)

DBoth

Explanation

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

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