Algebra 2 — Semester B Practice

Question 1 of 10

Massachusetts 6M-6PEasy Diagram

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

ARational function

BLinear function

CPolynomial

DAbsolute value

Explanation

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

Question 2 of 10

Massachusetts 7A-7IEasy Diagram

Match the end behavior to a possible polynomial.

Af(x) = x

Bf(x) = x³ − 1

Cf(x) = −x⁴ + 1

Df(x) = x⁴ − 2x²

Explanation

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

Question 3 of 10

Massachusetts 8A-8CEasy Diagram

Identify the conic.

AParabola

BCircle

CEllipse

DHyperbola

Explanation

Equal radii in all directions → a circle.

Question 4 of 10

Massachusetts 8A-8CMedium Diagram

Which conic section is shown?

AEllipse

BHyperbola

CCircle

DParabola

Explanation

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

Question 5 of 10

Massachusetts 5A-5CMedium Diagram

Which equation matches this exponential graph?

Ay = log₂(x)

By = x²

Cy = (1/2)ˣ (decay)

Dy = 2ˣ (growth)

Explanation

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

Question 6 of 10

Massachusetts 5A-5CEasy Diagram

Which graph shows exponential decay?

ANeither

BA (curve rising)

CB (curve falling toward x-axis)

DBoth

Explanation

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

Question 7 of 10

Massachusetts 7A-7IMedium Diagram

The graph shown most likely belongs to which polynomial?

AA line

BOdd-degree polynomial with positive leading coefficient

COdd degree, negative leading coefficient

DEven-degree polynomial

Explanation

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

Question 8 of 10

Massachusetts 8A-8CEasy Diagram

Which conic equation does this represent?

ACircle: x² + y² = r²

BHyperbola

CEllipse: x²/a² + y²/b² = 1

DParabola

Explanation

Oval shape stretched horizontally → ellipse with horizontal major axis.

Question 9 of 10

Massachusetts 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 10 of 10

Massachusetts 7A-7IEasy Diagram

How many real zeros does the polynomial graph show?

A2 real zeros

B1 real zero

C3 real zeros

D4 real zeros

Explanation

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

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