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Graph each of the following polynomials on your own piece of paper or using graphing software like Desmos. What is similar about them? What is different? For each of these questions, select all that apply.

a) $f(x) = 6 x^{6} + 3 x - 5$
b) $g(x) = 6 x^{6} + 2x$
c) $h(x) = 6 x^{6} + 8$

What is similar?

A. They all have a leading coefficient of 6.
B. For each, as $x$ goes to $+ \infty$ , the function goes to $+\infty$ .
C. For each, as $x$ goes to $- \infty$ , the function goes to $+\infty$ .
D. They are all degree 6 polynomials.
E. For each, as $x$ goes to $- \infty$ , the function goes to $-\infty$ .
F. For each, as $x$ goes to $+ \infty$ , the function goes to $-\infty$ .
G. They all have 2 terms
H. They all have only one $x$ -intercept.

What is different?

A. They have different $y$ intercepts.
B. They have a different number of terms.
C. They have different $x$ -intercepts.
D. They have different leading coefficients.
E. They are different degree polynomials.
F. They have different long-run behaviors.

Hint

Make sure you graph the functions to get all of the possible answers.

You should also compare the equations themselves.