Unit 1/2 Review

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Which of the following is the definition of a function? A relation where each input has exactly one output, A relation where each output has exactly one input, A relation where inputs and outputs can be paired in any way, A relation with only positive numbers

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A relation where each input has exactly one output

Answer explanation

A function is defined as a relation where each input corresponds to exactly one output. This ensures that for every value you input, there is a unique result, making option A the correct choice.

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Answer explanation

The y-intercept of a linear function is the value of f(x) when x=0. For f(x) = 3x - 5, substituting x=0 gives f(0) = 3(0) - 5 = -5. Thus, the y-intercept is -5.

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Answer explanation

To solve for x in the equation 2x + 7 = 15, subtract 7 from both sides to get 2x = 8. Then, divide both sides by 2 to find x = 4. Thus, the correct answer is x = 4.

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Answer explanation

To solve |x - 4| = 7, we set up two equations: x - 4 = 7 and x - 4 = -7. Solving these gives x = 11 and x = -3. Thus, the solutions are x = 11 or x = -3.

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Answer explanation

The Slope-Intercept form of a linear equation is represented as y = mx + b, where m is the slope and b is the y-intercept. The other options represent different types of equations.

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Answer explanation

To find the x-intercept, set f(x) = 0: -x + 2 = 0. Solving gives x = 2. Thus, the x-intercept is at x = 2.

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Answer explanation

To solve the inequality 3x - 4 < 8, first add 4 to both sides: 3x < 12. Then, divide by 3: x < 4. Thus, the correct answer is x < 4.

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Answer explanation

To solve |2x - 1| ≤ 5, we split it into two inequalities: 2x - 1 ≤ 5 and 2x - 1 ≥ -5. Solving these gives -2 ≤ x ≤ 3, which matches the correct choice: -2 ≤ x ≤ 3.

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Answer explanation

To find the equation of the line through (1, 2) and (3, 6), calculate the slope: (6-2)/(3-1) = 2. Using point-slope form, y - 2 = 2(x - 1) simplifies to y = 2x. Thus, the correct answer is y = 2x.

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Answer explanation

To solve |3x + 2| = 4x - 1, consider two cases: 3x + 2 = 4x - 1 and -(3x + 2) = 4x - 1. Solving the first gives x = 3. The second case leads to no valid solutions. Thus, the correct answer is x = 3.