Algebra 2 — Semester B Practice

Question 1 of 10

TEKS 6M-6P Medium Diagram

Identify the vertical and horizontal asymptotes.

A No asymptotes

B VA: x = 2, HA: y = 3

C VA: y = 3, HA: x = 2

D VA: x = 3, HA: y = 2

Explanation

Dashed vertical line at x = 3 (denominator zero) and dashed horizontal at y = 2 (degrees equal, leading-coefficient ratio).

Question 2 of 10

TEKS 5A-5C Medium Diagram

Identify the graph.

A Exponential decay: y = (1/2)ˣ

B Logarithmic

C Quadratic

D Linear

Explanation

Curve starts high on the left, approaches zero on the right — classic exponential decay.

Question 3 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 4 of 10

TEKS 7A-7I Easy Diagram

How many real zeros does the polynomial graph show?

A 3 real zeros

B 4 real zeros

C 1 real zero

D 2 real zeros

Explanation

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

Question 5 of 10

TEKS 5A-5C Medium Diagram

Which equation matches this exponential graph?

A y = log₂(x)

B y = x²

C y = 2ˣ (growth)

D y = (1/2)ˣ (decay)

Explanation

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

Question 6 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 Polynomial

B Linear function

C Rational function (has both VA and HA)

D Absolute value

Explanation

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

Question 7 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 8 of 10

TEKS 7A-7I Medium Diagram

What are the degree (parity) and leading-coefficient sign of this polynomial?

A Even degree, positive leading coefficient

B Even degree, negative leading coefficient

C Odd degree, negative leading coefficient

D Odd degree, positive leading coefficient

Explanation

Both ends rise to +∞ → even degree with positive leading coefficient.

Question 9 of 10

TEKS 5A-5C Easy Diagram

Which graph shows exponential decay?

A Neither

B Both

C B (curve falling toward x-axis)

D A (curve rising)

Explanation

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

Question 10 of 10

TEKS 7A-7I Medium Diagram

The graph shown most likely belongs to which polynomial?

A Even-degree polynomial

B A line

C Odd-degree polynomial with negative leading coefficient

D Odd-degree polynomial with positive leading coefficient

Explanation

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

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