Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 01, 2023

Find the degree and leading coefficient of $f(x)=5x-4$ , and state the end behavior of its graph.

STEP 1

Assumptions1. The given function is $f(x)=5x-4$ . The degree of a polynomial is the highest power of x in its terms3. The leading coefficient of a polynomial is the coefficient of the term with the highest power of x4. The end behavior of a function refers to the behavior of the graph as x approaches positive infinity ( $x \rightarrow \infty$ ) and negative infinity ( $x \rightarrow -\infty$ )

STEP 2

First, we need to identify the degree of the function. The degree of a polynomial is the highest power of x in its terms.In the given function $f(x)=5x-4$ , the highest power of x is1. Therefore, the degree of the function is1.

STEP 3

Now, let's identify the leading coefficient of the function. The leading coefficient of a polynomial is the coefficient of the term with the highest power of x.
In the given function $f(x)=5x-$ , the coefficient of the term with the highest power of x (which is $x^1$ ) is5. Therefore, the leading coefficient of the function is5.

STEP 4

Now, let's determine the end behavior of the function. The end behavior of a function refers to the behavior of the graph as x approaches positive infinity ( $x \rightarrow \infty$ ) and negative infinity ( $x \rightarrow -\infty$ ).
Since the degree of the function is odd (1) and the leading coefficient is positive (), as $x \rightarrow \infty$ , $f(x) \rightarrow \infty$ and as $x \rightarrow -\infty$ , $f(x) \rightarrow -\infty$ .
So, the end behavior of the function is as $x \rightarrow \infty$ , $f(x) \rightarrow \infty$ and as $x \rightarrow -\infty$ , $f(x) \rightarrow -\infty$ .
(a) The degree of $f$ is1 and its leading coefficient is. (b) The end behavior of the graph of $f$ is as $x \rightarrow \infty$ , $f(x) \rightarrow \infty$ and as $x \rightarrow -\infty$ , $f(x) \rightarrow -\infty$ .

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