Graph Transformations and Function Properties

Which of the following statements is true about functions?

• A function can have multiple outputs for a single input.

• A function must have a graph representation.

• A function can have only one output for each input.

• A function is always represented by an equation.

In an arithmetic sequence, what is the term used to describe the difference between consecutive terms?

• Geometric mean

• Recursive formula

• Common difference

• Common ratio

How do you determine if a sequence is geometric?

• By checking if the difference between terms is constant.

• By checking if the ratio between terms is constant.

• By checking if the sequence is defined recursively.

• By checking if the sequence is increasing at a constant rate.

Which of the following is true about solving linear equations involving fractions?

• You can always use a calculator to find the exact value.

• Fractions should be converted to decimals for easier calculation.

• Linear equations with fractions are always simple to solve.

• The exact value of x can be messy and should not be rounded.

What happens to a graph when you add a constant directly to the x variable?

• The graph shifts horizontally in the opposite direction.

• The graph becomes narrower.

• The graph becomes wider.

• The graph shifts vertically.

When completing the square, what is the purpose of adding a specific number to the equation?

• To convert the equation into a linear form.

• To eliminate the x variable from the equation.

• To ensure the trinomial is a perfect square.

• To make the equation easier to solve using a calculator.

What is the new vertex of the parabola y = x^2 after it is shifted 6 units to the right and 29 units down?

• (6, -29)

• (0, -29)

• (6, 0)

• (0, 0)

Which of the following is a correct factorization of the expression P^4 - 81?

• (P^2 - 9)(P^2 + 9)

• (P^2 - 3)(P^2 + 3)

• (P - 9)(P + 9)

• (P^2 + 3)(P^2 - 3)

Which of the following numbers is a perfect square?

• 100

• 81

• 89

• 256

What is the primary purpose of using the quadratic formula?

• To simplify expressions

• To complete the square

• To find the roots of any quadratic equation

• To factor quadratic equations