The table represents some points on the graph of linear function "f"f.

Question

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