Question

The table represents some points on the graph of linear function "f"f.
x
negative 2
f(x)
negative 224
Which function represents "f"f?

"f" left parenthesis, "x" , right parenthesis equals 32 left parenthesis, 3 "x" minus 1 , right parenthesis
"f" left parenthesis, "x" , right parenthesis equals negative 32 left parenthesis, "x" minus 3 , right parenthesis
"f" left parenthesis, "x" , right parenthesis equals negative 2 left parenthesis, 32 "x" minus 3 , right parenthesis
"f" left parenthesis, "x" , right parenthesis equals 16 left parenthesis, 2 "x" minus 1 , right parenthesis

Answer 1

To determine which function represents \( f(x) \) given that \( f(-2) = -224 \), we need to evaluate each option and see which one fits this condition.

1. **Option A**: \( f(x) = 32(3x - 1) \)
\[
f(-2) = 32(3(-2) - 1) = 32(-6 - 1) = 32(-7) = -224
\]
This option satisfies the condition.

2. **Option B**: \( f(x) = -32(x - 3) \)
\[
f(-2) = -32(-2 - 3) = -32(-5) = 160
\]
This option does not satisfy the condition.

3. **Option C**: \( f(x) = -2(32x - 3) \)
\[
f(-2) = -2(32(-2) - 3) = -2(-64 - 3) = -2(-67) = 134
\]
This option does not satisfy the condition.

4. **Option D**: \( f(x) = 16(2x - 1) \)
\[
f(-2) = 16(2(-2) - 1) = 16(-4 - 1) = 16(-5) = -80
\]
This option does not satisfy the condition.

After evaluating all options, only **Option A** satisfies the condition \( f(-2) = -224 \):

\[
f(x) = 32(3x - 1)
\]

Thus, the function that represents \( f \) is:
\[
f(x) = 32(3x - 1)
\]