Algebra 2 — Semester B Practice

Question 1 of 10

Massachusetts 7A-7IEasy Diagram

Match the end behavior to a possible polynomial.

Af(x) = x⁴ − 2x²

Bf(x) = −x⁴ + 1

Cf(x) = x³ − 1

Df(x) = x

Explanation

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

Question 2 of 10

Massachusetts 5A-5CEasy Diagram

Which graph shows exponential growth?

ANeither

BBoth

CA — curve rising more steeply

DB — curve falling toward x-axis

Explanation

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

Question 3 of 10

Massachusetts 8A-8CEasy Diagram

Identify the conic.

AEllipse

BHyperbola

CParabola

DCircle

Explanation

Equal radii in all directions → a circle.

Question 4 of 10

Massachusetts 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

Massachusetts 7A-7IEasy Diagram

How many real zeros does the polynomial graph show?

A2 real zeros

B1 real zero

C4 real zeros

D3 real zeros

Explanation

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

Question 6 of 10

Massachusetts 7A-7IMedium Diagram

The graph shown most likely belongs to which polynomial?

AOdd-degree polynomial with positive leading coefficient

BEven-degree polynomial

CA line

DOdd degree, negative leading coefficient

Explanation

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

Question 7 of 10

Massachusetts 6M-6PEasy Diagram

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

AAbsolute value

BPolynomial

CLinear function

DRational function

Explanation

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

Question 8 of 10

Massachusetts 5A-5CEasy Diagram

Which graph shows exponential decay?

ABoth

BNeither

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 9 of 10

Massachusetts 8A-8CMedium Diagram

Which conic section is shown?

ACircle

BParabola

CHyperbola

DEllipse

Explanation

Two separate branches that open left and right indicate a hyperbola with horizontal transverse axis: x²/a² − y²/b² = 1.

Question 10 of 10

Massachusetts 8A-8CEasy Diagram

Which conic equation does this represent?

AParabola

BHyperbola

CEllipse: x²/a² + y²/b² = 1

DCircle: x² + y² = r²

Explanation

Oval shape stretched horizontally → ellipse with horizontal major axis.

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