Question

1. solve the inequality $-5 < x + 2 < 3$. graph the solution on the number line.

1. what is the range of the function $f(x) = x^2 + 3$ if the domain is ${0, 1, 4, 9}$?

1. determine whether each graphs domain is discrete or continuous.

1. if $f(x) = 2x - 5$, what is the value of $f(6)$?

1. find the value of $f(x)=7$.

1. a music website charges $x$ dollars for individual songs and $y$ dollars for entire albums. person a pays $25.92$ to download 6 individual songs and 2 albums. person b pays $33.93$ to download 4 individual songs and 3 albums. use $s$ for the cost of each song and $a$ for the cost of each album. write a system of equations to represent the situation.

Explanation:

Question 14: Solve the inequality \(-5 < x + 2 < 3\)

Step 1: Subtract 2 from all parts

To isolate \(x\), we subtract 2 from each part of the compound inequality.
\[
-5 - 2 < x + 2 - 2 < 3 - 2
\]

Step 2: Simplify each part

Simplify the left, middle, and right parts of the inequality.
\[
-7 < x < 1
\]

Step 1: Find \(f(0)\)

Substitute \(x = 0\) into \(f(x)\):
\[
f(0)=0^{2}+3 = 3
\]

Step 2: Find \(f(1)\)

Substitute \(x = 1\) into \(f(x)\):
\[
f(1)=1^{2}+3=1 + 3=4
\]

Step 3: Find \(f(4)\)

Substitute \(x = 4\) into \(f(x)\):
\[
f(4)=4^{2}+3 = 16+3=19
\]

Step 4: Find \(f(9)\)

Substitute \(x = 9\) into \(f(x)\):
\[
f(9)=9^{2}+3=81 + 3=84
\]

Step 5: Determine the range

The range is the set of all output values, so we collect the results from Step 1 to Step 4.

Step 1: Substitute \(x = 6\) into \(f(x)\)

Replace \(x\) with 6 in the function \(f(x)=2x - 5\).
\[
f(6)=2(6)-5
\]

Step 2: Simplify the expression

First, calculate \(2(6)=12\), then subtract 5.
\[
f(6)=12 - 5=7
\]

Answer:

\(-7 < x < 1\)

Question 15: Range of \(f(x)=x^{2}+3\) with domain \(\{0,1,4,9\}\)