Question

vertical is the y - axis
in f(4)=-10 the input was 4 and the output was -10
the points (-4, 5) and (-4, 2) show a horizontal shift of left 3
the points (-10, 2) and (-10, -3) show a vertical shift of down 5
reflections change the size and shape of the parent function
if f(9)=7 this would mean the ordered pair (7, 9)
translations will not change the size or shape of a

Explanation:

Step1: Analyze vertical axis statement

In a coordinate - plane, the vertical axis is the y - axis. So, "Vertical is the y - axis" is True.

Step2: Analyze function input - output statement

For a function \(y = f(x)\), when \(x = 4\) and \(y=-10\) (i.e., \(f(4)=-10\)), the input is 4 and the output is - 10. This statement is True.

Step3: Analyze horizontal shift statement

The points \((-4,5)\) and \((-4,2)\) have the same x - coordinate. There is no horizontal shift; it is a vertical change. This statement is False.

Step4: Analyze vertical shift statement

For the points \((-10,2)\) and \((-10,-3)\), the x - coordinate is the same. The change in the y - coordinate is \(2-(-3)=5\), which means a vertical shift down 5. This statement is True.

Step5: Analyze reflection statement

Reflections change the orientation of the parent function but not its size and shape. This statement is False.

Step6: Analyze function ordered - pair statement

If \(f(9) = 7\), the ordered pair is \((9,7)\) not \((7,9)\). This statement is False.

Step7: Analyze translation statement

Translations (shifts) only move the function and do not change its size or shape. This statement is True.

Answer:

1. True
2. True
3. False
4. True
5. False
6. False
7. True