Graphing Exponential Function in Exercise ,sketch the graph of the function.See example 3 and 4.

Mathematics

1 answer:

9966 [12]3 years ago

7 0

Answer:

The graph is attached below.

Step-by-step explanation:

Considering the exponential function

$y=3^{-2x}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{bx}=\left(a^b\right)^x$

$3^{-2x}=\left(3^2\right)^{-x}$

$=\left(3^2\right)^{-x}$

$=9^{-x}$

The graph is also attached below.

Keywords: exponential function, graph

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Determined if the graph represents a polynomial function if it does determine the number of turning points and the least degree

skelet666 [1.2K]

<em>The graph of f is a polynomial function</em>
<em>There are two turning points, namely, x = 0 and x = -2</em>

<h2>Explanation:</h2>

A polynomial function in one variable is given by the form:

$f(x)=a_{n}x^n+a_{n-1}x^{n-1}+\cdots +a_{2}x^2+a_{1}x+a_{0}$

Since you haven't provided any expression, I'll choose the following function:

$f(x)=x^{3}+3x^{2}+3$

So this is indeed a polynomial function. A turning point is an x-value where we have either a local maximum or local minimum. So we need to take the derivative of this functions:

$f'(x)=3x^2+6x \\ \\ Finding \ turning \ points: \\ \\ 3x^2+6x=0 \\ \\ x(3x+6)=0 \\ \\ \\ So: \\ \\ x=0 \\ \\ and \\ \\ \ 3x+6=0 \therefore \ \boxed{x=-2}$