Question

Which function has the greatest value for X = 20?(1 point)
A;
X, f(x)
0,0
1,5
2,10
3,15
4,20
B:
x, g(x)
0,0
1,1
2,4
3,9
4,16
C:
x, h(x)
0,0
1,1
2,8
3,27
4,64
D:
x, p(x)
0,1
1,2
2,4
3,8
4,16

Answer 1

To determine which function has the greatest value for \( X = 20 \), we first need to identify the relationships defined by each function:

**A**: This function appears to be linear,

\[
f(x) = 5x \text{ for } x \in [0, 4]
\]

For \( X = 20 \):

\[
f(20) = 5 \times 20 = 100
\]

---

**B**: This function represents the square of x,

\[
g(x) = x^2 \text{ for } x \in [0, 4]
\]

For \( X = 20 \):

\[
g(20) = 20^2 = 400
\]

---

**C**: This function appears to be based on cubes of x,

\[
h(x) = x^3 \text{ for } x \in [0, 4]
\]

For \( X = 20 \):

\[
h(20) = 20^3 = 8000
\]

---

**D**: This function is based on powers of 2,

\[
p(x) = 2^x \text{ for } x \in [0, 4]
\]

For \( X = 20 \):

\[
p(20) = 2^{20} = 1048576
\]

---

Now we can summarize:

- \( f(20) = 100 \)
- \( g(20) = 400 \)
- \( h(20) = 8000 \)
- \( p(20) = 1048576 \)

Comparing these values, the greatest value among them is

\[
\boxed{1048576} \text{ from function D, } p(x) = 2^x.
\]