Algebra 2 — Semester 2 Practice — Michigan Test Out™

Question 1 of 10

Michigan Standards 7A-7IEasy Diagram

How many real zeros does the polynomial graph show?

A1 real zero

B2 real zeros

C4 real zeros

D3 real zeros

Explanation

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

Question 2 of 10

Michigan Standards 6M-6PEasy Diagram

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

ALinear function

BRational function

CAbsolute value

DPolynomial

Explanation

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

Question 3 of 10

Michigan Standards 7A-7IEasy Diagram

Match the end behavior to a possible polynomial.

Af(x) = x³ − 1

Bf(x) = x

Cf(x) = −x⁴ + 1

Df(x) = x⁴ − 2x²

Explanation

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

Question 4 of 10

Michigan Standards 5A-5CMedium Diagram

Which equation matches this exponential graph?

Ay = (1/2)ˣ (decay)

By = log₂(x)

Cy = 2ˣ (growth)

Dy = x²

Explanation

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

Question 5 of 10

Michigan Standards 5A-5CEasy Diagram

Which graph shows exponential growth?

ANeither

BB — curve falling toward x-axis

CBoth

DA — curve rising more steeply

Explanation

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

Question 6 of 10

Michigan Standards 8A-8CEasy Diagram

Identify the conic.

AHyperbola

BParabola

CCircle

DEllipse

Explanation

Equal radii in all directions → a circle.

Question 7 of 10

Michigan Standards 6M-6PEasy Diagram

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

AA parabola opening up

BA two-branch hyperbola in quadrants I and III

CA V-shape

DA line through the origin

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 8 of 10

Michigan Standards 5A-5CEasy Diagram

Which graph shows exponential decay?

ABoth

BA (curve rising)

CNeither

DB (curve falling toward x-axis)

Explanation

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

Question 9 of 10

Michigan Standards 8A-8CEasy Diagram

Which conic equation does this represent?

ACircle: x² + y² = r²

BHyperbola

CParabola

DEllipse: x²/a² + y²/b² = 1

Explanation

Oval shape stretched horizontally → ellipse with horizontal major axis.

Question 10 of 10

Michigan Standards 7A-7IMedium Diagram

The graph shown most likely belongs to which polynomial?

AOdd degree, negative leading coefficient

BOdd-degree polynomial with positive leading coefficient

CEven-degree polynomial

DA line

Explanation

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

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