Q1. State the domain and range of the relation. Determine whether the relation is a function or not. Then complete the mapping diagram: {(-2, 4), (5, 5), (-6, 8), (7, 5), (-10, -10), (7, -1)}

Background

Topic: Relations and Functions

This question tests your understanding of how to identify the domain and range from a set of ordered pairs, determine if the relation is a function, and represent the relation using a mapping diagram.

Key Terms:

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

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

• Function: A relation in which each input (x) is paired with exactly one output (y).

Step-by-Step Guidance

1. List all the x-values from the given pairs to find the domain.

2. List all the y-values from the given pairs to find the range.

3. Check if any x-value is paired with more than one y-value. If so, the relation is not a function.

4. Draw a mapping diagram by connecting each x-value to its corresponding y-value.

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Q2. For the function :

• a. Write the function.

• c. Find .

• d. State the domain.

• e. State the range.

Background

Topic: Function Evaluation and Properties

This question tests your ability to evaluate a function for a given expression, and to determine the domain and range of a linear function.

Key Terms and Formulas:

• Function Evaluation: Substitute the input value or expression into the function.

• Domain of Linear Function: Usually all real numbers unless restricted.

• Range of Linear Function: Usually all real numbers unless restricted.

Step-by-Step Guidance

1. Write the function as .

2. To find , substitute for in the function.

3. For domain and range, consider the properties of linear functions.

4. Set up the expressions for domain and range, but do not compute the final values yet.

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Q3. Find the difference quotient of

Background

Topic: Difference Quotient

This question tests your ability to compute the difference quotient, which is foundational for understanding rates of change and derivatives.

Key Formula:

• Difference Quotient:

Step-by-Step Guidance

1. Write the formula for the difference quotient.

2. Find by substituting into the function.

3. Subtract from .

4. Set up the expression for the difference quotient, but do not simplify to the final answer yet.

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Q4. Find the difference quotient of

Background

Topic: Difference Quotient for Rational Functions

This question tests your ability to apply the difference quotient to a rational function, which is important for understanding more complex rates of change.

Key Formula:

• Difference Quotient:

Step-by-Step Guidance

1. Write the formula for the difference quotient.

2. Find by substituting into the function.

3. Subtract from .

4. Set up the expression for the difference quotient, but do not simplify to the final answer yet.

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Q10. Given the following equations, determine if the function is even, odd, or neither. Then determine its symmetry:

Background

Topic: Even and Odd Functions, Symmetry

This question tests your ability to classify functions as even, odd, or neither, and to determine their symmetry (y-axis, origin, or neither).

Key Terms:

• Even Function: for all (symmetric about the y-axis).

• Odd Function: for all (symmetric about the origin).

• Neither: If neither condition is met.

Step-by-Step Guidance

1. For each function, substitute for and simplify.

2. Compare to and to determine if the function is even, odd, or neither.

3. Identify the type of symmetry based on your classification.

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Q12. Find the average rate of change of over the interval .

Background

Topic: Average Rate of Change

This question tests your ability to calculate the average rate of change of a function over a specified interval, which is foundational for understanding slopes and derivatives.

Key Formula:

• Average Rate of Change: , where and are the endpoints of the interval.

Step-by-Step Guidance

1. Identify and .

2. Calculate and by substituting and into the function.

3. Set up the formula .

4. Do not compute the final value yet; set up the expressions for and .

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Q13. Be able to sketch the following parent functions on a graph:

• Square root function

• Cube root function

• Absolute (Value) function

• Constant function

• Identity function

• Square (Quadratic) function

• Cube function

• Reciprocal (rational) function

Background

Topic: Parent Functions and Graphs

This question tests your ability to recognize and sketch the basic shapes of parent functions, which is essential for understanding transformations and graphing.

Key Terms:

• Parent Function: The simplest form of a function type.

• Graph: Visual representation of the function.

Step-by-Step Guidance

1. Recall the basic shape and formula for each parent function.

2. Identify key points (such as intercepts and symmetry) for each graph.

3. Sketch or describe the general appearance of each graph.

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