Unit 0 Day 5 Assignment

State the domain and range of the following set of ordered pairs: {$(-3, 5),\ (0, 2),\ (1, 7),\ (4, -2),\ (1, 9)$}

Is the relation given in Q1 a function? Explain your reasoning using the fundamental rule of input/output mapping.

A vertical line crosses a graphed relation at $(2, 4)$ and $(2, -1)$. Does this graph represent a function? Justify your response using the Vertical Line Test (VLT).

Consider a vending machine where pressing button $A1$ sometimes dispenses a giant mallet and other times dispenses a laughing gas canister. Explain mathematically why this machine fails to operate as a function.

Given the function $f(x) = -4x + 9$, find the exact value of $f(-3)$.

Given the function $g(x) = 2x^2 - 3x + 1$, evaluate $g(4)$.

If $h(x) = \dfrac{24}{x} - 5$, evaluate $h(-6)$. State what value of $x$ is excluded from the domain of $h(x)$.

For the function rule $f(x) = 3x + 2$, if the output value $f(x) = 17$, what was the corresponding input value $x$?

A linear function has a continuous graph that starts at the point $(-2,-5)$ with a solid circle and ends at the point $(4,7)$ with an open circle. State its domain and range using interval notation.

Consider the sequence: $11, 7, 3, -1, -5, \ldots$ Identify whether it is arithmetic, and calculate the common difference ($d$).

Write the explicit formula for the arithmetic sequence: $5, 12, 19, 26, \ldots$

Recall: $a_n = a_1 + (n - 1)d$

Using your explicit formula from $Q11$, find the value of the 52nd term ($a_{52}$).

Write the recursive formula for the sequence given in $Q10$.

Format: State $a_1$ and the rule for $a_n$ based on $a_{n-1}$.

An arithmetic sequence has a first term of $a_1 = -15$ and a common difference of $d = 6$. Which position number ($n$) yields a term value equal to $33$?

Determine the common ratio ($r$) for the following geometric sequence: $3,\ -6,\ 12,\ -24,\ 48,\ \dots$

Write the explicit formula for the geometric sequence: $4,\ 20,\ 100,\ 500,\ \dots$

Recall: $a_n = a_1 \cdot r^{n-1}$

Find the exact 7th term ($a_7$) of the geometric sequence: $1024,\ 512,\ 256,\ 128,\ \dots$

Write the recursive formula for the geometric sequence: $-2,\ -8,\ -32,\ -128,\ \dots$

Identify the type of sequence (Arithmetic or Geometric), find its parameters ($d$ or $r$), and find the next term for:

$2,\ 3,\ 4.5,\ 6.75,\ \dots$

Harley Quinn decides to track her total savings inside Arkham over several weeks. On week 1, she has $50. Every week after, she increases her savings geometrically by multiplying the previous week's total by a ratio of $1.2$. How much money will she have accumulated on week 5? Round your answer to the nearest cent.