Question

1. a mapping is shown in the diagram below. diagram of mapping between months (jan, feb, mar, apr) and numbers (28, 29, 30, 31) this mapping is a. a function, because feb has two outputs, 28 and 29 b. a function, because two inputs, jan and mar, result in the output 31 c. not a function, because feb has two outputs, 28 and 29 d. not a function, because two inputs, jan and mar, result in the output 31 2. if the domain of the function $f(x) = 2x^2 - 8$ is ${-2, 3, 5}$, then the range is a. ${-16, 4, 92}$ b. ${-16, 10, 42}$ c. ${0, 10, 42}$ d. ${0, 4, 92}$ 3. the function $g(x)$ is defined as $g(x) = -2x^2 + 3x$. the value of $g(-3)$ is a. -27 b. -9 c. 27 d. 45 handwritten work: $-2x^2 + 3x$; $-2(-3)^2 + 3(-3)$

Explanation:

Question 1

Step1: Recall Function Definition

A function is a relation where each input (from the domain) has exactly one output (in the codomain).

Step2: Analyze Each Option

• Option A: Claims it's a function, but Feb has two outputs (28, 29) – violates function definition. Eliminate.
• Option B: Claims it's a function, but multiple inputs (Jan, Mar) to one output is allowed in relations, but the issue is Feb's multiple outputs. Eliminate.
• Option C: Correct. Feb (input) has two outputs, so not a function.
• Option D: Incorrect. Multiple inputs to one output doesn't violate function definition; the violation is Feb's multiple outputs.

Step1: Recall Range Definition

Range is the set of outputs \( f(x) \) for given domain inputs.

Step2: Calculate \( f(x) \) for Each Domain Value

• For \( x = -2 \): \( f(-2) = 2(-2)^2 - 8 = 2(4) - 8 = 8 - 8 = 0 \)
• For \( x = 3 \): \( f(3) = 2(3)^2 - 8 = 2(9) - 8 = 18 - 8 = 10 \)
• For \( x = 5 \): \( f(5) = 2(5)^2 - 8 = 2(25) - 8 = 50 - 8 = 42 \)

Step3: Determine Range

The range is \( \{0, 10, 42\} \).

Step1: Substitute \( x = -3 \) into \( g(x) \)

Given \( g(x) = -2x^2 + 3x \), substitute \( x = -3 \):

Step2: Calculate Each Term

• \( -2(-3)^2 = -2(9) = -18 \)
• \( 3(-3) = -9 \)

Step3: Sum the Terms

\( g(-3) = -18 + (-9) = -27 \)

Answer:

C. not a function, because Feb has two outputs, 28 and 29

Question 2