Question

you will create a picture by graphing a variety of equations or inequalities. Be creative and artistic with this cross-curricular project.

You must use AT LEAST 10 equations/inequalities in your picture.

You must find and use the inverse of AT LEAST 1 function.

Your picture must be colorful or outlined in different colors.

List the equations/inequalities that you used in creating your picture, including any restrictions on x (or y).

Identify the inverse function by using the inverse symbol

You may use linear, absolute value, quadratic, square root, cube root, cubic functions, or other polynomials. You may also use points.

Make sure to number the graphs in your picture to correspond to the respective equation/inequality.

Answer 1

$1)\; y_1 - 3x - 1 = 0, \; x,y_3\in \R$

$2)\; y_2+4= x^2, \; x \in \R, y_2 \in [-4;+\infty)$

$3) \; y_3=\sqrt{5x}, \; x\in[0; +\infty), y_3\in[0; +\infty)$

$4)\; y_4-3|x+3|=0, \; x \in \R, y_4\in[0;+\infty)$

$5) \; y_5 = \dfrac{x^2}{5}= y_3^{-1}, \;x,y_5\in[0;+\infty)$ (we decide here to consider $x\in[0;+\infty)$ instead of $x\in\R$ )

$6)\; y_6 - \dfrac{x^3}{10}=0, \; x,y_6\in\R$

$7) \; (x+4)^2+(y-14)^2 \le 0 \Rightarrow x=-4, y=14$

$8) \; y_8 = |x|-x^3, \; x,y_8\in\R$

$9) \; y_9 -x^2-\sqrt{x} = 7,\; x,y_9\in[0; +\infty)$

$10) \; |x+8|+|y_{10}-7| \le 0 \Rightarrow x=-8, y_{10}=7$

$11)\; y_{11}^2=121 \Rightarrow y_{11}=\pm11, x\in \R$