Algebra 2 — Semester B Practice

Question 1 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 2 of 10

NYS 6M-6PEasy Diagram

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

AA V-shape

BA line through the origin

CA parabola opening up

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 5A-5CEasy Diagram

Which graph shows exponential decay?

ANeither

BBoth

CB (curve falling toward x-axis)

DA (curve rising)

Explanation

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

Question 4 of 10

NYS 7A-7IEasy Diagram

How many real zeros does the polynomial graph show?

A2 real zeros

B3 real zeros

C1 real zero

D4 real zeros

Explanation

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

Question 5 of 10

NYS 7A-7IMedium Diagram

The graph shown most likely belongs to which polynomial?

AEven-degree polynomial

BA line

COdd degree, negative leading coefficient

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 6 of 10

NYS 5A-5CEasy Diagram

Which graph shows exponential growth?

ABoth

BA — curve rising more steeply

CB — curve falling toward x-axis

DNeither

Explanation

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

Question 7 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

CRational function

DPolynomial

Explanation

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

Question 8 of 10

NYS 8A-8CEasy Diagram

Which conic equation does this represent?

AParabola

BCircle: x² + y² = r²

CEllipse: x²/a² + y²/b² = 1

DHyperbola

Explanation

Oval shape stretched horizontally → ellipse with horizontal major axis.

Question 9 of 10

NYS 8A-8CEasy Diagram

Identify the conic.

AEllipse

BHyperbola

CCircle

DParabola

Explanation

Equal radii in all directions → a circle.

Question 10 of 10

NYS 5A-5CMedium Diagram

Which equation matches this exponential graph?

Ay = x²

By = log₂(x)

Cy = 2ˣ (growth)

Dy = (1/2)ˣ (decay)

Explanation

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

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