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?

A4 real zeros

B1 real zero

C2 real zeros

D3 real zeros

Explanation

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

Question 2 of 10

Michigan Standards 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 3 of 10

Michigan Standards 5A-5CMedium Diagram

Which equation matches this exponential graph?

Ay = log₂(x)

By = x²

Cy = 2ˣ (growth)

Dy = (1/2)ˣ (decay)

Explanation

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

Question 4 of 10

Michigan Standards 5A-5CEasy Diagram

Which graph shows exponential decay?

AA (curve rising)

BNeither

CBoth

DB (curve falling toward x-axis)

Explanation

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

Question 5 of 10

Michigan Standards 7A-7IEasy Diagram

Match the end behavior to a possible polynomial.

Af(x) = −x⁴ + 1

Bf(x) = x

Cf(x) = x³ − 1

Df(x) = x⁴ − 2x²

Explanation

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

Question 6 of 10

Michigan Standards 6M-6PEasy Diagram

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

ARational function

BPolynomial

CLinear function

DAbsolute value

Explanation

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

Question 7 of 10

Michigan Standards 7A-7IMedium Diagram

The graph shown most likely belongs to which polynomial?

AOdd-degree polynomial with positive leading coefficient

BEven-degree polynomial

COdd degree, negative leading coefficient

DA line

Explanation

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

Question 8 of 10

Michigan Standards 6M-6PEasy Diagram

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

AA two-branch hyperbola in quadrants I and III

BA V-shape

CA parabola opening up

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 9 of 10

Michigan Standards 8A-8CEasy Diagram

Which conic equation does this represent?

AParabola

BCircle: x² + y² = r²

CHyperbola

DEllipse: x²/a² + y²/b² = 1

Explanation

Oval shape stretched horizontally → ellipse with horizontal major axis.

Question 10 of 10

Michigan Standards 8A-8CEasy Diagram

Identify the conic.

AHyperbola

BEllipse

CCircle

DParabola

Explanation

Equal radii in all directions → a circle.

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