# Functions

```Problem Set D:
y
g(x) = ( 2 x − 3)1 4 + 1
1.
In the function above, for what values of x
is g(x) a real number?
(A) x ≥ 0
(B) x ≥ 1/2
(C) x ≥ 3/2
(D) x ≥ 2
(E) x ≥ 3
(–1, 0)
5.
2.
x
–1
0
1
2
f(x)
1
3
1
–5
The table above shows the values of the
quadratic function f for several values of x.
Which one of the following best represents
f?
(A)
(B)
f (x) = −2 x
2
2
f (x) = x + 3
2
(C)
f (x) = − x + 3
(D)
f (x) = −2 x 2 − 3
(E)
2
In the function above, if f(k) = 2, then
which one of the following could be a value
of k ?
(A) –1
(B) 0
(C) 0.5
(D) 2.5
(E) 4
Let the function h be defined by
h(x) = x + 2 . If 3h(v) = 18, then which
v
one of the following is the value of h   ?
 4
(A) –4
(B) –1
(C) 0
(D) 2
(E) 4
(B)
x = − y2
(C)
x = − y2 + 1
(D)
x = y2 − 1
(E)
x = ( y + 1)
2
2
At time t = 0, a projectile was fired upward
from an initial height of 10 feet. Its height
after t seconds is given by the function
h(t) = p − 10(q − t) 2 , where p and q are
positive constants. If the projectile reached
a maximum height of 100 feet when t = 3,
then what was the height, in feet, of the
projectile when t = 4 ?
(A) 62 (B) 70 (C) 85 (D) 89 (E) 90
y = f (x)
4.
x = − ( y + 1)
7.
y
3.
(A)
A pottery store owner determines that the
revenue for sales of a particular item can be
modeled by the function r(x) = 50 x − 40,
where x is the number of the items sold.
How many of the items must be sold to
generate \$110 in revenue?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
f (x) = −2 x + 3
x
The graph above shows a parabola that is
symmetric about the x-axis. Which one of
the following could be the equation of the
graph?
6.
2
1
x
O
y
A
D O
8.
y = a − x2
B
C
x
The figure above shows the graph of
y = a − x 2 for some constant a . If the
square ABCD intersects the graph at points
A and B and the area of the square is 16,
what is the value of a ?
(A) 2 (B) 4 (C) 6 (D) 8 (E) 10
```