Algebra 2 — Semester B Practice

Question 1 of 10

TEKS 6M-6P Easy Diagram

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

A A V-shape

B A parabola opening up

C A two-branch hyperbola in quadrants I and III

D A 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 2 of 10

TEKS 6M-6P Easy Diagram

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

A Rational function

B Polynomial

C Absolute value

D Linear function

Explanation

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

Question 3 of 10

TEKS 8A-8C Easy Diagram

Which conic equation does this represent?

A Circle: x² + y² = r²

B Hyperbola

C Ellipse: x²/a² + y²/b² = 1

D Parabola

Explanation

Oval shape stretched horizontally → ellipse with horizontal major axis.

Question 4 of 10

TEKS 7A-7I Easy Diagram

How many real zeros does the polynomial graph show?

A 1 real zero

B 3 real zeros

C 4 real zeros

D 2 real zeros

Explanation

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

Question 5 of 10

TEKS 7A-7I Easy Diagram

Match the end behavior to a possible polynomial.

A f(x) = x⁴ − 2x²

B f(x) = x³ − 1

C f(x) = x

D f(x) = −x⁴ + 1

Explanation

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

Question 6 of 10

TEKS 5A-5C Easy Diagram

Which graph shows exponential growth?

A A — curve rising more steeply

B B — curve falling toward x-axis

C Both

D Neither

Explanation

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

Question 7 of 10

TEKS 5A-5C Easy Diagram

Which graph shows exponential decay?

A A (curve rising)

B Neither

C B (curve falling toward x-axis)

D Both

Explanation

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

Question 8 of 10

TEKS 8A-8C Easy Diagram

Identify the conic.

A Hyperbola

B Ellipse

C Parabola

D Circle

Explanation

Equal radii in all directions → a circle.

Question 9 of 10

TEKS 5A-5C Medium Diagram

Which equation matches this exponential graph?

A y = 2ˣ (growth)

B y = x²

C y = log₂(x)

D y = (1/2)ˣ (decay)

Explanation

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

Question 10 of 10

TEKS 7A-7I Medium Diagram

The graph shown most likely belongs to which polynomial?

A Odd degree, negative leading coefficient

B A line

C Odd-degree polynomial with positive leading coefficient

D Even-degree polynomial

Explanation

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

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