Question

On a coordinate plane, a straight line with a negative slope, labeled f of x, crosses the y-axis at (0, 4), and the x-axis at (4, 0).
Which is true regarding the graphed function f(x)?

f of 0 = 3
f of 5 = negative 1
f of 3 = 2
f of 2 = negative 2Consider the function represented by with x as the independent variable. How can this function be written using function notation?




If point (4, 5) is on the graph of a function, which equation must be true?

f(5)=4
f(5,4)=9
f(4)=5
f(5,4)=1The function g(x) is graphed.

On a coordinate plane, a curved line enters the plane at point (negative 2.3, 5), crosses the x- and y-axis at (0, 0), and leaves the plane at point (2.3, 5).

Which statements about the function are true? Choose three options.

g of 1 = negative 1
g of 0 = 0
g of 4 = negative 2
g of 1 = 1
g of negative 1 = 1The point (–3, –5) is on the graph of a function. Which equation must be true regarding the function?

f(–3) = –5
f(–3, –5) = –8
f(–5) = –3
f(–5, –3) = –2The height of a rocket a given number of seconds after it is released is modeled by h (t) = negative 16 t squared + 32 t + 10. What does t represent?

the number of seconds after the rocket is released
the initial height of the rocket
the initial velocity of the rocket
the height of the rocket after t secondsThe function f(x) is given by the set of ordered pairs.

{(8, –3), (0, 4), (1, –5), (2, –1), (–6, 10)}

Which is true regarding the function?

f(–3) = 8
f(3) = 5
f(8) = 0
f(–6) = 10Consider the function represented by the equation 6q = 3s - 9. Write the equation in function notation, where q is the independent variable.

f of q = one-half q minus three-halves
f(q) = 2s + 3
f of s = one-half s minus three-halves
f(q) = 2q + 3Consider the function represented by the table.



The ordered pair given in the bottom row can be written using function notation as

f(9)=5.
f(5)=9.
f(5, 9)=14.
f(9, 5)=14.Consider the function represented by the table.



For which x is f(x)=–3?

–7
–4
4
5

Answer 1

Here are the answers with brief justifications:

1) Line through (0,4) and (4,0): equation y = -x + 4. Which is true?
- f(5) = -1 (because f(5) = -5 + 4 = -1).

2) "Consider the function represented by y with x as the independent variable. How can this function be written using function notation?"
- Write y as f(x); i.e., y = f(x).

3) If (4,5) is on the graph, which equation must be true?
- f(4) = 5.

4) For g(x) entering at (-2.3,5), passing through (0,0), leaving at (2.3,5): choose three true statements:
- g(0) = 0
- g(1) = 1
- g(-1) = 1
(Shape is symmetric with origin as lowest point, so values at ±1 are equal and positive.)

5) If (–3, –5) is on the graph, which equation must be true?
- f(–3) = –5.

6) In h(t) = -16t^2 + 32t + 10, what does t represent?
- the number of seconds after the rocket is released.

7) For f(x) given by {(8, –3), (0, 4), (1, –5), (2, –1), (–6, 10)} which is true?
- f(–6) = 10.

8) From 6q = 3s - 9, write in function notation where q is independent:
- f(q) = 2q + 3 (solve for s as the dependent variable: s = 2q + 3).

9) From the table where the bottom row is (9, 5), written in function notation:
- f(9) = 5.

10) From the table (choices: –7, –4, 4, 5), for which x is f(x) = –3?
- 4.