Answer the questions below to determine what kind of function is depicted in the table belov x & 1 & 2 & 3 & 4 & 5 f(x) & -13 & -26 & -52 & -104 & -208 Answer Attempt 1 out of 2 This function is square because

## Step 1: Identify the Pattern<br />### Observe the values of \( f(x) \) as \( x \) increases. Notice that each value of \( f(x) \) is a multiple of the previous one, specifically doubling each time. This suggests an exponential relationship or a geometric progression.<br /><br />## Step 2: Determine the Function Type<br />### Calculate the ratio between consecutive terms of \( f(x) \):<br />- From \( f(1) = -13 \) to \( f(2) = -26 \), the ratio is \(\frac{-26}{-13} = 2\).<br />- From \( f(2) = -26 \) to \( f(3) = -52 \), the ratio is \(\frac{-52}{-26} = 2\).<br />- From \( f(3) = -52 \) to \( f(4) = -104 \), the ratio is \(\frac{-104}{-52} = 2\).<br />- From \( f(4) = -104 \) to \( f(5) = -208 \), the ratio is \(\frac{-208}{-104} = 2\).<br /><br />### Since the ratio is constant, this indicates a geometric sequence where each term is multiplied by a constant factor (in this case, 2). However, since the function is linear in terms of multiplication by a constant factor, it can also be represented as a linear function with respect to powers of 2.<br /><br />## Step 3: Formulate the Function<br />### Given the pattern, the function can be expressed as:<br />\[ f(x) = -13 \times 2^{x-1} \]<br />This is because when \( x = 1 \), \( f(x) = -13 \times 2^{0} = -13 \), and similarly for other values of \( x \).