Algebra 2 — Semester 2 Practice — Michigan Test Out™

Question 1 of 10

Michigan Standards 5A-5CEasy Diagram

Which graph shows exponential decay?

AB (curve falling toward x-axis)

BA (curve rising)

CBoth

DNeither

Explanation

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

Question 2 of 10

Michigan Standards 6M-6PEasy Diagram

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

AA parabola opening up

BA V-shape

CA two-branch hyperbola in quadrants I and III

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 3 of 10

Michigan Standards 5A-5CEasy Diagram

Which graph shows exponential growth?

AB — curve falling toward x-axis

BNeither

CBoth

DA — curve rising more steeply

Explanation

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

Question 4 of 10

Michigan Standards 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 5 of 10

Michigan Standards 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 6 of 10

Michigan Standards 7A-7IEasy Diagram

Match the end behavior to a possible polynomial.

Af(x) = −x⁴ + 1

Bf(x) = x

Cf(x) = x⁴ − 2x²

Df(x) = x³ − 1

Explanation

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

Question 7 of 10

Michigan Standards 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

Michigan Standards 5A-5CMedium Diagram

Which equation matches this exponential graph?

Ay = 2ˣ (growth)

By = x²

Cy = log₂(x)

Dy = (1/2)ˣ (decay)

Explanation

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

Question 9 of 10

Michigan Standards 8A-8CEasy Diagram

Identify the conic.

ACircle

BEllipse

CParabola

DHyperbola

Explanation

Equal radii in all directions → a circle.

Question 10 of 10

Michigan Standards 6M-6PEasy Diagram

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

AAbsolute value

BLinear function

CRational function

DPolynomial

Explanation

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

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