PARCC Algebra I Building Functions. Practice it free.

The common difference is $d = 3$. With $a_1 = 1$, the $16$th term is $a_{16} = 1 + 15(3) = 46$.

Work from the outside in. Since $p(5) = 1$, we need $q(r(x)) = 5$. Since $q(4) = 5$, we need $r(x) = 4$. From the table, $r(3) = 4$, so $x = 3$.

Following the pattern:
1st term, or $n = 1\textsf{:}$ $3 \cdot \left(\dfrac{1}{2}\right)^{0}$
2nd term, or $n = 2\textsf{:}$ $3 \cdot \left(\dfrac{1}{2}\right)^{1}$
3rd term, or $n = 3\textsf{:}$ $3 \cdot \left(\dfrac{1}{2}\right)^{2}$
4th term, or $n = 4\textsf{:}$ $3 \cdot \left(\dfrac{1}{2}\right)^{3}$
Since each term has an exponent that is $1$ less than the term number, the $n$th term is $w = 3 \cdot \left(\dfrac{1}{2}\right)^{n-1}$.

Start with the inner function: $-4 \leq 2$, so $f(-4)=|-4|-1=3$. Then $3 \geq 1$, so $g(3)=4-3=1\textsf{.}$

The common ratio is $\dfrac{18}{6} = 3\textsf{.}$ From the third term to the sixth term there are $3$ steps, so the sixth term is $18 \times 3^{3} = 486\textsf{.}$

Set $y = \dfrac{x - 4}{3}\textsf{.}$ Swap: $x = \dfrac{y - 4}{3}\textsf{.}$ Multiply by $3$ and add $4\textsf{:}$ $y = 3x + 4\textsf{.}$ So $f^{-1}(x) = 3x + 4\textsf{.}$

Replacing $x$ with $3x$ means outputs occur at one-third the original input values, so the graph is compressed horizontally by a factor of $\dfrac{1}{3}$.

To shift left, $x$ gets smaller but the height stays the same, so $4$ is added inside $f$. That is why you see $(x + 4)$.