Functions and function notation  (Page 10/21)

Why does the horizontal line test tell us whether the graph of a function is one-to-one?

$\left\{\left(a,b\right),\left(c,d\right),\left(a,c\right)\right\}$

$\{(a,b),(b,c),(c,c)\}$

$5x+2y=10$

$y=x^2$

$x=y^2$

$3x^2+y=14$

$2x+y^2=6$

$y=-2x^2+40x$

$y=\frac{1}{x}$

$x=\frac{3y+5}{7y-1}$

$x=\sqrt{1-y^2}$

$y=\frac{3x+5}{7x-1}$

$x^2+y^2=9$

$2xy=1$

$x=y^3$

$y=x^3$

$y=\sqrt{1-x^2}$

$x=\pm \sqrt{1-y}$

$y=\pm \sqrt{1-x}$

$y^2=x^2$

$y^3=x^2$

$f(x)=2x-5$

$f(x)=-5x^2+2x-1$

$f(x)=\sqrt{2-x}+5$

$f(x)=\frac{6x-1}{5x+2}$

$f(x)=\left|x-1\right|-\left|x+1\right|$

Given the function $g(x)=5-x^2,$ evaluate $\frac{g(x+h)-g(x)}{h},h\ne 0.$

Given the function $g(x)=x^2+2x,$ evaluate $\frac{g(x)-g(a)}{x-a},x\ne a.$

Given the function $k(t)=2t-1:$

1. Evaluate $k(2).$
2. Solve $k(t)=7.$

Given the function $f(x)=8-3x:$

1. Evaluate $f(-2).$
2. Solve $f(x)=-1.$

Given the function $p(c)=c^2+c:$

1. Evaluate $p(-3).$
2. Solve $p(c)=2.$

Given the function $f(x)=x^2-3x:$

1. Evaluate $f(5).$
2. Solve $f(x)=4.$

Given the function $f(x)=\sqrt{x+2}:$

1. Evaluate $f(7).$
2. Solve $f(x)=4.$

Consider the relationship $3r+2t=18.$

1. Write the relationship as a function $r=f(t).$
2. Evaluate $f(-3).$
3. Solve $f(t)=2.$

Given the following graph,

• Evaluate $f(\mathrm{-1}).$
• Solve for $f(x)=3.$

Given the following graph,

• Evaluate $f(0).$
• Solve for $f(x)=\mathrm{-3.}$

Given the following graph,

• Evaluate $f(4).$
• Solve for $f(x)=1.$

$\left\{\left(\mathrm{-1},\mathrm{-1}\right),\left(\mathrm{-2},\mathrm{-2}\right),\left(\mathrm{-3},\mathrm{-3}\right)\right\}$

$\left\{\left(3,4\right),\left(4,5\right),\left(5,6\right)\right\}$

$\left\{(2,5),(7,11),(15,8),(7,9)\right\}$

Evaluate $f(3).$

Solve $f(x)=1.$

$f\left(x\right)=4-2x$

$f\left(x\right)=8-3x$

$f\left(x\right)=8x^2-7x+3$

$f\left(x\right)=3+\sqrt{x+3}$

$f(x)=\frac{x-2}{x+3}$

$f\left(x\right)=3^x$

$3f\left(1\right)-4g\left(-2\right)$

$f\left(\frac{7}{3}\right)-h\left(-2\right)$

$[-0.1,0.1]$

$[-10,\text{ 10}]$

$[-100,100]$

$[-0.1,\text{ 0}\text{.1}]$

$[-10,\text{ 10}]$

$[-100,\text{ 100}]$

$[0,\text{ 0}\text{.01}]$

$[0,\text{ 100}]$

$[0,\text{ 10,000}]$

$[\mathrm{-0.001},\text{0.001}]$

$[\mathrm{-1000},\text{1000}]$

$[\mathrm{-1,000,000},\text{1,000,000}]$

The amount of garbage, $G,$ produced by a city with population $p$ is given by $G=f\left(p\right).$ $G$ is measured in tons per week, and $p$ is measured in thousands of people.

1. The town of Tola has a population of 40,000 and produces 13 tons of garbage each week. Express this information in terms of the function $f.$
2. Explain the meaning of the statement $f\left(5\right)=2.$

The number of cubic yards of dirt, $D,$ needed to cover a garden with area $a$ square feet is given by $D=g\left(a\right).$

1. A garden with area 5000 ft ² requires 50 yd ³ of dirt. Express this information in terms of the function $g.$
2. Explain the meaning of the statement $g\left(100\right)=1.$

Let $f\left(t\right)$ be the number of ducks in a lake $t$ years after 1990. Explain the meaning of each statement:

1. $f\left(5\right)=30$
2. $f\left(10\right)=40$

Let $h\left(t\right)$ be the height above ground, in feet, of a rocket $t$ seconds after launching. Explain the meaning of each statement:

1. $h\left(1\right)=200$
2. $h\left(2\right)=350$

Show that the function $f\left(x\right)=3{\left(x-5\right)}^2+7$ is not one-to-one.