Question

Suppose that

f
(
x
)
=
x
2
+
6
x
−
5
. Notice that
f
(
9
)
=
21.75
. What does this tell us about the numerator and denominator of
f
?

When
x
=
21.75
,
x
2
+
6
is 9 times as large as
x
−
5
.
When
x
=
9
,
x
2
+
6
is 21.75 times as large as
x
−
5
.
When
x
=
9
,
x
−
5
is 21.75 times as large as
x
2
+
6
.
When
x
=
9
,
x
2
+
6
is equal to 21.75.

x
2
+
6
is always 21.75 times as large as
x
−
5
.

Answer 1

When x = 9, the function f(x) = x^2 + 6x - 5 equals 21.75, meaning the portion x^2 + 6x is 21.75 times as large as x - 5 when x is 9.

Step-by-step explanation:

If we are given that f(x) = x2 + 6x - 5 and f(9) = 21.75, this means when we substitute x = 9 into the function f(x), the resulting value is 21.75.

This does not, however, provide direct information about the relationship between various components of the function such as the numerator and the denominator as the function given doesn't inherently have a fraction form.

Considering the options given, the correct interpretation is that when x = 9, the value of x2 + 6x is equal to 21.75 times as large as the value of x - 5.

This is because, when we substitute x = 9 into the function f(x), we are essentially saying (92 + 6*9) / (9 - 5) = 21.75, which means (81 + 54) / 4 = 21.75, and so 135/4 = 21.75.