Q1. Which set of ordered pairs does not represent a function?

Background

Topic: Functions and Relations

This question tests your understanding of what makes a relation a function, specifically the requirement that each input (x-value) must correspond to exactly one output (y-value).

Key Terms:

• Function: A relation in which each input has exactly one output.

• Ordered Pair: A pair of numbers (x, y) representing a point in the coordinate plane.

Step-by-Step Guidance

1. Look at each set of ordered pairs and identify the x-values in each set.

2. Check if any x-value is repeated with a different y-value in the same set. If so, that set does not represent a function.

3. Recall: If a single x-value is paired with more than one y-value, the relation is not a function.

4. Go through each answer choice and list the x-values to check for repeats.

Try solving on your own before revealing the answer!

Q2. Determine whether the following graph represents a function.

Background

Topic: Functions and the Vertical Line Test

This question asks you to use the vertical line test to determine if a graph represents a function.

Key Terms:

• Vertical Line Test: A graph represents a function if and only if no vertical line intersects the graph at more than one point.

Step-by-Step Guidance

1. Visualize or draw vertical lines at various x-values on the graph.

2. Check if any vertical line crosses the graph at more than one point.

3. If a vertical line crosses the graph more than once, the graph does not represent a function.

Try solving on your own before revealing the answer!

Q3. Find the value of f(7) from the given graph.

Background

Topic: Evaluating Functions from Graphs

This question tests your ability to read a graph and find the output value for a given input.

Key Terms:

• Function Notation: f(x) represents the output of the function when the input is x.

Step-by-Step Guidance

1. Locate x = 7 on the x-axis of the graph.

2. Move vertically from x = 7 to the point on the graph.

3. Read the corresponding y-value at that point. This is f(7).

Try solving on your own before revealing the answer!

Q4. Find the domain of the function defined by the set of points below. Express your answer as a set of numbers.

Background

Topic: Domain of a Function

This question asks you to identify all possible input values (x-values) for a function given as a set of points.

Key Terms:

• Domain: The set of all possible input values (x-values) for a function.

Step-by-Step Guidance

1. List all the x-values from the given set of points.

2. Write the domain as a set, using curly braces { } and listing the x-values in order.

3. Check for any repeated x-values and list each only once.

Try solving on your own before revealing the answer!

Q5. Find the range of the function defined by the set of points below. Express your answer as a set of numbers.

Background

Topic: Range of a Function

This question asks you to identify all possible output values (y-values) for a function given as a set of points.

Key Terms:

• Range: The set of all possible output values (y-values) for a function.

Step-by-Step Guidance

1. List all the y-values from the given set of points.

2. Write the range as a set, using curly braces { } and listing the y-values in order.

3. Check for any repeated y-values and list each only once.

Try solving on your own before revealing the answer!

Q6. Determine the domain of the following graph.

Background

Topic: Domain from a Graph

This question tests your ability to find the set of all x-values for which the graph is defined.

Key Terms:

• Domain: The set of all x-values for which the function is defined (where the graph exists horizontally).

Step-by-Step Guidance

1. Look at the leftmost and rightmost points of the graph to determine the interval of x-values covered.

2. Check if the graph includes endpoints (closed or open circles) to decide if the interval is open or closed.

3. Write the domain as an interval or set, as appropriate.

Try solving on your own before revealing the answer!

Q7. Determine the range of the following graph.

Background

Topic: Range from a Graph

This question tests your ability to find the set of all y-values for which the graph is defined.

Key Terms:

• Range: The set of all y-values for which the function is defined (where the graph exists vertically).

Step-by-Step Guidance

1. Look at the lowest and highest points on the graph to determine the interval of y-values covered.

2. Check if the graph includes endpoints (closed or open circles) to decide if the interval is open or closed.

3. Write the range as an interval or set, as appropriate.

Try solving on your own before revealing the answer!

Q8. Determine the range of the following graph.

Background

Topic: Range from a Graph

This question tests your ability to find the set of all y-values for which the graph is defined.

Key Terms:

• Range: The set of all y-values for which the function is defined (where the graph exists vertically).

Step-by-Step Guidance

1. Look at the lowest and highest points on the graph to determine the interval of y-values covered.

2. Check if the graph includes endpoints (closed or open circles) to decide if the interval is open or closed.

3. Write the range as an interval or set, as appropriate.

Try solving on your own before revealing the answer!

Q9. Factor x^2 + 2x - 15

Background

Topic: Factoring Quadratic Expressions

This question tests your ability to factor a quadratic trinomial into two binomials.

Key Formula:

Standard form:

Factored form: where and are numbers that multiply to and add to .

Step-by-Step Guidance

1. Identify , , and in the quadratic expression.

2. Find two numbers that multiply to and add to $2$.

3. Write the factored form as using those numbers.

Try solving on your own before revealing the answer!