Algebra 2 — Semester B Practice

Question 1 of 10

NYS 8A-8CEasy Diagram

Which conic equation does this represent?

AParabola

BEllipse: x²/a² + y²/b² = 1

CCircle: x² + y² = r²

DHyperbola

Explanation

Oval shape stretched horizontally → ellipse with horizontal major axis.

Question 2 of 10

NYS 6M-6PEasy Diagram

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

AA line through the origin

BA parabola opening up

CA V-shape

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 7A-7IEasy Diagram

How many real zeros does the polynomial graph show?

A1 real zero

B4 real zeros

C3 real zeros

D2 real zeros

Explanation

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

Question 4 of 10

NYS 8A-8CEasy Diagram

Identify the conic.

AEllipse

BParabola

CHyperbola

DCircle

Explanation

Equal radii in all directions → a circle.

Question 5 of 10

NYS 5A-5CEasy Diagram

Which graph shows exponential decay?

ABoth

BA (curve rising)

CB (curve falling toward x-axis)

DNeither

Explanation

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

Question 6 of 10

NYS 5A-5CEasy Diagram

Which graph shows exponential growth?

ABoth

BA — curve rising more steeply

CNeither

DB — curve falling toward x-axis

Explanation

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

Question 7 of 10

NYS 7A-7IEasy Diagram

Match the end behavior to a possible polynomial.

Af(x) = x⁴ − 2x²

Bf(x) = x

Cf(x) = x³ − 1

Df(x) = −x⁴ + 1

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 = 2ˣ (growth)

Dy = log₂(x)

Explanation

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

Question 9 of 10

NYS 7A-7IMedium Diagram

The graph shown most likely belongs to which polynomial?

AOdd degree, negative leading coefficient

BA line

CEven-degree polynomial

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 10 of 10

NYS 6M-6PEasy Diagram

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

APolynomial

BAbsolute value

CLinear function

DRational function

Explanation

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

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