Algebra 2 — Semester B Practice

Question 1 of 10

NYS 7A-7IEasy Diagram

Match the end behavior to a possible polynomial.

Af(x) = x³ − 1

Bf(x) = x

Cf(x) = x⁴ − 2x²

Df(x) = −x⁴ + 1

Explanation

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

Question 2 of 10

NYS 7A-7IMedium Diagram

The graph shown most likely belongs to which polynomial?

AOdd degree, negative leading coefficient

BOdd-degree polynomial with positive leading coefficient

CA line

DEven-degree polynomial

Explanation

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

Question 3 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

BLinear function

CPolynomial

DRational function

Explanation

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

Question 4 of 10

NYS 5A-5CMedium Diagram

Which equation matches this exponential graph?

Ay = x²

By = 2ˣ (growth)

Cy = (1/2)ˣ (decay)

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.

AParabola

BHyperbola

CCircle

DEllipse

Explanation

Equal radii in all directions → a circle.

Question 6 of 10

NYS 5A-5CEasy Diagram

Which graph shows exponential growth?

AB — curve falling toward x-axis

BBoth

CA — curve rising more steeply

DNeither

Explanation

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

Question 7 of 10

NYS 5A-5CEasy Diagram

Which graph shows exponential decay?

AB (curve falling toward x-axis)

BBoth

CA (curve rising)

DNeither

Explanation

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

Question 8 of 10

NYS 7A-7IEasy Diagram

How many real zeros does the polynomial graph show?

A4 real zeros

B1 real zero

C3 real zeros

D2 real zeros

Explanation

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

Question 9 of 10

NYS 6M-6PEasy Diagram

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

AA two-branch hyperbola in quadrants I and III

BA line through the origin

CA V-shape

DA parabola opening up

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 10 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.

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