StudyBlaze

Building a Foundation

1. What is the definition of a function? (1 choice)

D) A relation with multiple inputs and outputs

A) A relation where each input is related to multiple outputs

B) A relation where each input is related to exactly one output

C) A relation with no outputs

2. Which of the following are characteristics of a function? (multiple choice)

B) The graph passes the Vertical Line Test

C) Each output has exactly one input

D) The graph can be crossed by a vertical line more than once

A) Each input has exactly one output

3. Explain the Vertical Line Test and how it is used to determine if a graph represents a function.

4. List the types of functions mentioned in the key concepts.

What are linear functions?

What are quadratic functions?

What are polynomial functions?

Your answers will be evaluated by AI for key concepts, not exact wording. Focus on main ideas.

Comprehension and Application

5. Given the quadratic function y = x^2 - 4x + 4, find the vertex of the parabola.

6. What is the domain of a function? (1 choice)

B) The set of all possible inputs

D) The set of all possible constants

A) The set of all possible outputs

C) The set of all possible variables

7. Which of the following are true about linear functions? (multiple choice)

A) They form a straight line on a graph

B) They have the form y = mx + b

C) They form a V-shaped curve

D) They represent exponential growth

8. Describe the difference between the domain and range of a function with an example.

9. Given the function f(x) = 2x + 3, what is f(4)? (1 choice)

A) 11

B) 8

C) 10

D) 9

10. Identify which of the following graphs represent a function. (multiple choice)

B) A graph of a circle

C) A graph of a parabola

A) A graph of a straight line

D) A graph of a V-shaped curve

Analysis, Evaluation, and Creation

11. Evaluate the following scenarios and determine which can be represented by a function. (multiple choice)

C) The relationship between distance and time for a constant speed

D) The relationship between a book's title and its author

B) The relationship between a person's age and height

A) The relationship between temperature and time of day

12. Create a real-world scenario where a quadratic function could be used to model the situation. Explain why a quadratic function is appropriate.

13. If a function f(x) has an inverse, what must be true about its graph? (1 choice)

A) It must be a straight line

B) It must pass the Horizontal Line Test

D) It must have no intercepts

C) It must be a parabola

14. Analyze the function y = |x|. Which of the following are true? (multiple choice)

A) It is a linear function

B) It forms a V-shaped graph

C) It has a vertex at the origin

D) It is not a function

15. Compare and contrast linear and quadratic functions in terms of their graphs and equations.

16. Which of the following statements is true about inverse functions? (1 choice)

A) They do not exist for linear functions

C) They have the same graph as the original function

B) They reverse the operation of the original function

D) They are always quadratic

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