Question

2-95. write a possible equation for each of these graphs. assume that one mark on each axis is one unit. when you are in class, check your equations on a graphing calculator and compare your results with your teammates.
a.
b.
c.
d.
e.
f.
g.
h.
i.

Explanation:

Step1: Identify graph a (hyperbola)

This is a reciprocal function, with vertical asymptote $x=-1$, horizontal asymptote $y=0$, and passes through $(0,1)$.
$y=\frac{1}{x+1}$

Step2: Identify graph b (parabola)

Upward-opening parabola, vertex at $(0,-4)$, width matches $y=x^2$.
$y=x^2 - 4$

Step3: Identify graph c (cubic)

Cubic function with a double root at $x=1$, passes through $(0,-2)$.
$y=2(x-1)^2(x+1)$

Step4: Identify graph d (exponential)

Exponential growth function, passes through $(0,-1)$ and $(1,1)$, base 2.
$y=2^x - 2$

Step5: Identify graph e (linear)

Linear function with slope 1, y-intercept -4.
$y=x - 4$

Step6: Identify graph f (cube root)

Horizontal shift left 2, vertical stretch by 2, shift up 1.
$y=2\sqrt[3]{x+2}+1$

Step7: Identify graph g (parabola)

Upward-opening parabola, vertex at $(-3,-4)$.
$y=(x+3)^2 - 4$

Step8: Identify graph h (quadratic)

Downward-opening parabola, roots at $x=-1, x=4$, vertex at $(1.5, 6.25)$.
$y=-(x+1)(x-4)$

Step9: Identify graph i (cube root)

Horizontal shift right 1, vertical stretch by 2, shift up 1.
$y=2\sqrt[3]{x-1}+1$

Answer:

a. $y=\frac{1}{x+1}$
b. $y=x^2 - 4$
c. $y=2(x-1)^2(x+1)$
d. $y=2^x - 2$
e. $y=x - 4$
f. $y=2\sqrt[3]{x+2}+1$
g. $y=(x+3)^2 - 4$
h. $y=-(x+1)(x-4)$
i. $y=2\sqrt[3]{x-1}+1$