Algebra 2 — Semester 2 Practice — Michigan Test Out™

Question 1 of 10

Michigan Standards 8A-8CEasy Diagram

Identify the conic.

AParabola

BEllipse

CCircle

DHyperbola

Explanation

Equal radii in all directions → a circle.

Question 2 of 10

Michigan Standards 8A-8CEasy Diagram

Which conic equation does this represent?

AEllipse: x²/a² + y²/b² = 1

BParabola

CHyperbola

DCircle: x² + y² = r²

Explanation

Oval shape stretched horizontally → ellipse with horizontal major axis.

Question 3 of 10

Michigan Standards 6M-6PEasy Diagram

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

AA line through the origin

BA parabola opening up

CA V-shape

DA two-branch hyperbola in quadrants I and III

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 4 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 5 of 10

Michigan Standards 7A-7IMedium Diagram

The graph shown most likely belongs to which polynomial?

AA line

BOdd degree, negative leading coefficient

CEven-degree polynomial

DOdd-degree polynomial with positive leading coefficient

Explanation

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

Question 6 of 10

Michigan Standards 5A-5CEasy Diagram

Which graph shows exponential growth?

AA — curve rising more steeply

BB — curve falling toward x-axis

CBoth

DNeither

Explanation

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

Question 7 of 10

Michigan Standards 5A-5CMedium Diagram

Which equation matches this exponential graph?

Ay = (1/2)ˣ (decay)

By = 2ˣ (growth)

Cy = x²

Dy = log₂(x)

Explanation

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

Question 8 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

BPolynomial

CRational function

DLinear function

Explanation

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

Question 9 of 10

Michigan Standards 7A-7IEasy Diagram

Match the end behavior to a possible polynomial.

Af(x) = x³ − 1

Bf(x) = x⁴ − 2x²

Cf(x) = x

Df(x) = −x⁴ + 1

Explanation

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

Question 10 of 10

Michigan Standards 5A-5CEasy Diagram

Which graph shows exponential decay?

AA (curve rising)

BB (curve falling toward x-axis)

CNeither

DBoth

Explanation

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

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