Question

how does a bee get to school?
circle the letter of each correct answer in the boxes below. the circled letters will spell out the answer to the riddle.
evaluate the function for the given value of x.

1. $g(x)=x - 7;x = 4$ $g(4)=-3$
2. $f(x)=-2x;x=-6$ $f(-6)=12$
3. $k(x)=-\frac{3}{4}x - 11;x=-12$ $k(-12)=-2$
4. $t(x)=9x + 10;x=-\frac{1}{6}$ $t(-\frac{1}{6})=\frac{1}{2}$
5. $g(x)=15-\frac{7}{8}x;x = 24$ $g(24)=-6$
6. $c(x)=0.25x - 3;x = 10$ $c(10)=-0.5$
7. $w(x)=21 - 6x - 13;x=\frac{1}{2}$ $w(\frac{1}{2})=5$
8. $p(x)=-\frac{1}{4}(x + 36)-14;x=-8$ $p(-8)=-21$

find the value of x so that the function has the given value.

1. $b(x)=8x;b(x)=-56$
2. $h(x)=-\frac{5}{6}x;h(x)=10$

in exercises 11 - 13, evaluate the function at the given values of the independent variables.

1. $f(x,y)=xy - 3y;f(-5,8)$
2. $f(x,y)=x + xy;f(6,5)$
3. $xoplus y=-4x - 9y + 1;3oplus - 2$
4. the local cable company charges $90 per month for basic cable and $12 per month for each additional premium cable channel. the function $c(x)=90 + 12x$ represents the monthly charge (in dollars), where x is the number of additional premium channels. how many additional premium channels would you have ordered if your bill was $114 per month?

Explanation:

Step1: Evaluate function for given x values

1. For \(g(x)=x - 7\) and \(x = 4\)

Substitute \(x = 4\) into \(g(x)\): \(g(4)=4 - 7=-3\)

2. For \(f(x)=-2x\) and \(x=-6\)

Substitute \(x=-6\) into \(f(x)\): \(f(-6)=-2\times(-6) = 12\)

3. For \(k(x)=-\frac{3}{4}x-11\) and \(x = - 12\)

Substitute \(x=-12\) into \(k(x)\): \(k(-12)=-\frac{3}{4}\times(-12)-11=9 - 11=-2\)

4. For \(t(x)=9x + 10\) and \(x=-\frac{1}{6}\)

Substitute \(x = -\frac{1}{6}\) into \(t(x)\): \(t(-\frac{1}{6})=9\times(-\frac{1}{6})+10=-\frac{3}{2}+10=\frac{-3 + 20}{2}=\frac{17}{2}\)

5. For \(g(x)=15-\frac{7}{8}x\) and \(x = 24\)

Substitute \(x = 24\) into \(g(x)\): \(g(24)=15-\frac{7}{8}\times24=15 - 21=-6\)

6. For \(c(x)=0.25x-3\) and \(x = 10\)

Substitute \(x = 10\) into \(c(x)\): \(c(10)=0.25\times10-3=2.5 - 3=-0.5\)

7. For \(w(x)=21-6x-13\) and \(x=\frac{1}{2}\)

First simplify \(w(x)=8 - 6x\), then substitute \(x=\frac{1}{2}\): \(w(\frac{1}{2})=8-6\times\frac{1}{2}=8 - 3 = 5\)

8. For \(p(x)=-\frac{1}{4}(x + 36)-14\) and \(x=-8\)

Substitute \(x=-8\) into \(p(x)\): \(p(-8)=-\frac{1}{4}(-8 + 36)-14=-\frac{1}{4}\times28-14=-7-14=-21\)

Step2: Find x when function has given value

9. For \(b(x)=8x\) and \(b(x)=-56\)

Set \(8x=-56\), then \(x=\frac{-56}{8}=-7\)

10. For \(h(x)=-\frac{5}{6}x\) and \(h(x)=10\)

Set \(-\frac{5}{6}x = 10\), then \(x=10\times(-\frac{6}{5})=-12\)

Step3: Evaluate two - variable functions

11. For \(f(x,y)=xy-3y\) and \(x=-5,y = 8\)

Substitute \(x=-5,y = 8\) into \(f(x,y)\): \(f(-5,8)=(-5)\times8-3\times8=-40-24=-64\)

12. For \(f(x,y)=x+xy\) and \(x = 6,y = 5\)

Substitute \(x = 6,y = 5\) into \(f(x,y)\): \(f(6,5)=6+6\times5=6 + 30=36\)

13. For \(x\star y=-4x-9y + 1\) and \(x = 3,y=-2\)

Substitute \(x = 3,y=-2\) into \(x\star y\): \(3\star(-2)=-4\times3-9\times(-2)+1=-12 + 18+1=7\)

Step4: Solve for x in application problem

14. For \(c(x)=90 + 12x\) and \(c(x)=114\)

Set \(90+12x=114\)
Subtract 90 from both sides: \(12x=114 - 90=24\)
Divide both sides by 12: \(x = 2\)

Answer:

1. \(g(4)=-3\)
2. \(f(-6)=12\)
3. \(k(-12)=-2\)
4. \(t(-\frac{1}{6})=\frac{17}{2}\)
5. \(g(24)=-6\)
6. \(c(10)=-0.5\)
7. \(w(\frac{1}{2})=5\)
8. \(p(-8)=-21\)
9. \(x=-7\)
10. \(x=-12\)
11. \(f(-5,8)=-64\)
12. \(f(6,5)=36\)
13. \(3\star(-2)=7\)
14. \(x = 2\)