Find the x and y intercepts for the function y = $$2x^2 + 11x - 6$$ .

x-intercept: (-3, 0) and (1, 0); y-intercept: (0, -6)

x-intercept: (3, 0) and (-1, 0); y-intercept: (0, 6)

x-intercept: (-2, 0) and (3, 0); y-intercept: (0, -6)

x-intercept: (2, 0) and (-3, 0); y-intercept: (0, 6)

Find the x and y intercepts for the function f(x) = $$\sqrt{2x + 3}$$ .

x-intercept: (-1.5, 0), y-intercept: (0, $$\sqrt{3}$$ )

x-intercept: (0, $$\sqrt{3}$$ ), y-intercept: (-1.5, 0)

x-intercept: (1.5, 0), y-intercept: (0, $$\sqrt{3}$$ )

x-intercept: (0, 1.5), y-intercept: ( $$\sqrt{3}$$ , 0)

Find the x and y intercepts for the graph in #3 above.

x-intercept: (3, 0), y-intercept: (0, 2)

x-intercept: (2, 0), y-intercept: (0, 3)

x-intercept: (0, 3), y-intercept: (3, 0)

x-intercept: (0, 2), y-intercept: (2, 0)

Part I: Find and classify all discontinuities for the function y = $$\frac{2x + 3}{x - 2}$$ .

The function has an infinite discontinuity at x = 2.

The function has a removable discontinuity at x = 2.

The function has a jump discontinuity at x = 2.

The function is continuous everywhere.

Part I: Find and classify all discontinuities for the function y = $$\frac{3x}{6 - 5x}$$ .

Infinite discontinuity at x = 6/5

Removable discontinuity at x = 6/5

Part I: Find and classify all discontinuities for the function f(x) = $$\frac{2x - 5}{x^2 - 9}$$ .

Infinite discontinuity at x = 3 and x = -3

Removable discontinuity at x = 3 and x = -3

Jump discontinuity at x = 3 and x = -3

Part I: Find and classify all discontinuities for the function g(x) = $$\frac{x^2 + x - 12}{x^2 + 11x + 28}$$ .

Removable discontinuities at x = -4 and x = -7

Removable discontinuity at x = -4, Jump discontinuity at x = -7

Jump discontinuity at x = -4, Removable discontinuity at x = -7

Jump discontinuities at x = -4 and x = -7

Part I: Find and classify all discontinuities for the function h(x) = $$\frac{3x - 1}{3x^2 + 5x - 2}$$ .

x = 1/3 and x = -2 are removable discontinuities

x = 1/3 is a removable discontinuity and x = -2 is a jump discontinuity

x = 1/3 is a jump discontinuity and x = -2 is a removable discontinuity

x = 1/3 and x = -2 are jump discontinuities

Part I: Find and classify all discontinuities for the function represented in the graph.

Removable discontinuity at x = 2, Jump discontinuity at x = 5

Jump discontinuity at x = 2, Infinite discontinuity at x = 5

Infinite discontinuity at x = 2, Removable discontinuity at x = 5

Removable discontinuity at x = 2, Infinite discontinuity at x = 5

Part II: Determine if the function f(x) = $$\begin{cases} x^3 + 3, & x

The function is not continuous at x = 0.

The function is continuous at x = 0.

The function is continuous for all x.

The function is not continuous for any x.

Determine if the function g(x) = $$\begin{cases} 7 - x, & x \leq 1 \\ \sqrt{x + 5x}, & x > 1 \end{cases}$$ is continuous at x = 1.

No, g(x) is not continuous at x = 1.

Yes, g(x) is continuous at x = 1.

Determine if the function h(x) = $$\begin{cases} 2^x, & x \leq 3 \\ x^2 - 1, & x > 3 \end{cases}$$ is continuous at x = 3.

No, h(x) is not continuous at x = 3.

Yes, h(x) is continuous at x = 3.

Example 1: For the graph below, find all discontinuities and classify each one by type.

Removable discontinuity at x = 2, Jump discontinuity at x = 5

Jump discontinuity at x = 2, Infinite discontinuity at x = 5

Infinite discontinuity at x = 2, Removable discontinuity at x = 5

Removable discontinuity at x = 2, Infinite discontinuity at x = 5

Example 2: Find all discontinuities for the function below and classify each one by type. $$f(x) = \frac{x^2 - 9}{x^2 + 8x + 15}$$

Removable discontinuity at x = -3 and x = -5

Jump discontinuity at x = 3 and x = 5

Infinite discontinuity at x = -3 and x = -5

Determine if the following functions are continuous at $$x = 3$$ . Which of the following statements is true? $$g(x) = \begin{cases} 2x - 1, & x 3 \end{cases}$$

Neither g(x) nor h(x) is continuous at x = 3.

Both g(x) and h(x) are continuous at x = 3.

Only g(x) is continuous at x = 3.

Only h(x) is continuous at x = 3.

Directions: For 1 – 7, find and classify all discontinuities for the functions below. 1. y = $$\frac{2x - 3}{x + 5}$$

Infinite discontinuity at x = -5

Removable discontinuity at x = -5

Directions: For 1 – 7, find and classify all discontinuities for the functions below. 2. y = $$\frac{3}{2 - 7x}$$

Infinite discontinuity at x = 2/7

Removable discontinuity at x = 2/7

Directions: For 1 – 7, find and classify all discontinuities for the functions below. 3. f(x) = $$\frac{2x}{x^2 - 1}$$

x = 1 and x = -1 are infinite discontinuities

x = 1 and x = -1 are removable discontinuities

x = 1 and x = -1 are jump discontinuities

x = 1 and x = -1 are oscillating discontinuities

Directions: For 1 – 7, find and classify all discontinuities for the functions below. 4. y = $$\frac{-1}{x^2 - x - 20}$$

x = 5 and x = -4 are infinite discontinuities

x = 5 and x = -4 are removable discontinuities

x = 5 and x = -4 are jump discontinuities

x = 5 and x = -4 are oscillating discontinuities

Directions: For 1 – 7, find and classify all discontinuities for the functions below. 5. g(x) = $$\frac{x^2 + 3x - 40}{x^2 + 10x + 16}$$

Removable discontinuity at x = -8 and x = -2

Jump discontinuity at x = -8 and x = -2

Infinite discontinuity at x = -8 and x = -2

Directions: For 1 – 7, find and classify all discontinuities for the functions below. 6. h(x) = $$\frac{2x - 3}{2x^2 - x - 3}$$

Removable discontinuity at x = 1

Infinite discontinuity at x = 1

Determine if the function h(x) = $$\begin{cases} x^3, & x \leq -2 \\ x^2 - 4, & x > -2 \end{cases}$$ is continuous at x = -2.

No, h(x) is not continuous at x = -2.

Yes, h(x) is continuous at x = -2.

Find the x and y intercepts of the relation shown in the graph.

x-intercept: (3, 0), y-intercept: (0, 2)

x-intercept: (2, 0), y-intercept: (0, 3)

x-intercept: (0, 3), y-intercept: (3, 0)

x-intercept: (0, 2), y-intercept: (2, 0)

Find the x and y intercepts of the relation shown in the graph.

x-intercept: (3, 0), y-intercept: (0, 2)

x-intercept: (2, 0), y-intercept: (0, 3)

x-intercept: (0, 3), y-intercept: (2, 0)

x-intercept: (0, 2), y-intercept: (3, 0)

Find the x and y intercepts of the function $$k(x) = x^4 - 9x^2$$ .

x-intercepts: (0,0), (3,0), (-3,0); y-intercept: (0,0)

x-intercepts: (0,0), (3,0), (-3,0); y-intercept: (0,9)

x-intercepts: (0,0), (3,0), (-3,0); y-intercept: (0,-9)

x-intercepts: (0,0), (3,0), (-3,0); y-intercept: (0,1)

Determine if the following function is continuous at x = 2. If not, name the type of discontinuity. Graph is provided.

The function is continuous at x = 2.

The function has a removable discontinuity at x = 2.

The function has a jump discontinuity at x = 2.

The function has an infinite discontinuity at x = 2.

Determine if the function f(x) = $$\{2x - 1, x

The function has a jump discontinuity at x = 2.

The function is continuous at x = 2.

The function has an infinite discontinuity at x = 2.

The function has a removable discontinuity at x = 2.

Determine if the function g(x) = $$\frac{x^2 + 5x + 6}{x^2 + x - 6}$$ is continuous at x = 2. If not, name the type of discontinuity.

Removable discontinuity at x = 2

Infinite discontinuity at x = 2

Worksheet A: 1.2 Analyzing Graphs

Authored by MAHESHWARI SRINIVASAN

Mathematics

11th Grade

Used 3+ times

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OPEN ENDED QUESTION

3 mins • 1 pt

Find the domain and range for the function y = h(x).

Evaluate responses using AI:

OFF

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the domain and range for the function y = h(x).

D: ________________ R: ________________

D: All real numbers R: All real numbers

D: x ≥ 0 R: y ≥ 0

D: x ≠ 0 R: y ≠ 0

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the domain and range for the function y = h(x).

D: ________________ R: ________________

D: All real numbers R: All real numbers

D: x ≥ 0 R: y ≥ 0

D: x ≠ 0 R: y ≠ 0

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the domain and range for the function y = h(x).

D: ________________ R: ________________

D: All real numbers R: All real numbers

D: x ≥ 0 R: y ≥ 0

D: x ≠ 0 R: y ≠ 0

OPEN ENDED QUESTION

3 mins • 1 pt

Find the domain and range for the function f(x).

Evaluate responses using AI:

OFF

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the domain and range for the function f(x).

D: ________________ R: ________________

D: All real numbers R: All real numbers

D: x ≥ 0 R: y ≥ 0

D: x ≠ 0 R: y ≠ 0

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

x-intercept: (7.5, 0), y-intercept: (0, 5)

x-intercept: (0, 7.5), y-intercept: (5, 0)

x-intercept: (5, 0), y-intercept: (0, 7.5)

x-intercept: (0, 5), y-intercept: (7.5, 0)

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