Question

answer the questions below to determine what kind of function is depicted in the table below.

$x$	$-3$	$-2$	$-1$	$0$	$1$
$f(x)$	$7$	$22$	$127$	$412$	$967$

answer attempt 1 out of 2

this function is because
none of the abo

exponential
quadratic
linear
none of the above

submit answer

Explanation:

To determine the function type, we check differences (for linear/quadratic) and ratios (for exponential).

• Linear Check: Calculate first differences (change in \( f(x) \)): \( 22 - 7 = 15 \), \( 127 - 22 = 105 \), \( 412 - 127 = 285 \), \( 967 - 412 = 555 \). Differences are not constant (15, 105, 285, 555), so not linear.
• Quadratic Check: Calculate second differences (change in first differences): \( 105 - 15 = 90 \), \( 285 - 105 = 180 \), \( 555 - 285 = 270 \). Second differences (90, 180, 270) are not constant (they increase by 90), so not quadratic.
• Exponential Check: Calculate ratios of \( f(x) \) values: \( \frac{22}{7} \approx 3.14 \), \( \frac{127}{22} \approx 5.77 \), \( \frac{412}{127} \approx 3.24 \), \( \frac{967}{412} \approx 2.35 \). Ratios are not constant, so not exponential.

Since the function is not linear, quadratic, or exponential, the answer is "none of the above".

Answer:

none of the above