Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Consider the following polynomial. $\newline$ $q(x)=4x^{2}-3x+12$ $\newline$ Step $2$ of $2$ : Describe the behavior of the graph of $q(x)$ as $x \rightarrow \pm\infty$ . $\newline$ $q(x)\rightarrow \square$ as $x \rightarrow -\infty$

View step-by-step help

View step-by-step help

Simplify radical expressions with variables II

Full solution

Q. Consider the following polynomial.

\newline

q(x)=4x^{2}-3x+12

\newline

Step

2

of

2

: Describe the behavior of the graph of

q(x)

as

x \rightarrow \pm\infty

.

\newline

q(x)\rightarrow \square

as

x \rightarrow -\infty

Identify Leading Term: To analyze the behavior of the graph of $q(x)$ as $x$ approaches positive or negative infinity, we need to consider the leading term of the polynomial $q(x) = 4x^2 - 3x + 12$ , which is $4x^2$ . The leading term will dominate the behavior of the polynomial for large values of $x$ , both positive and negative.
Behavior as $x$ approaches $+\infty$ : Since the leading coefficient of the leading term $4x^2$ is positive, as $x$ approaches positive infinity ( $x \rightarrow +\infty$ ), the value of $4x^2$ will also approach positive infinity. Therefore, $q(x)$ will approach positive infinity as well.
Behavior as $x$ approaches $-\infty$ : Similarly, as $x$ approaches negative infinity ( $x \rightarrow -\infty$ ), the value of $4x^2$ will still approach positive infinity because the square of a negative number is positive. Therefore, $q(x)$ will also approach positive infinity as $x$ approaches negative infinity.

More problems from Simplify radical expressions with variables II

Question

Order the expressions from least to greatest.

\newline

11^{1} \quad8^{2}-60 \quad 2^{2} \times 5

Posted 3 months ago

Question

Order the expressions from least to greatest.

\newline

2^{3}-2^{1} \quad 2^{1}+3^{1} \quad 3^{2}

Posted 3 months ago

Question

y=\sqrt{e^{x}}

\newline

\frac{d y}{d x}

\newline

1

\newline

\frac{\sqrt{e^{x}}}{2}

\newline

\sqrt{e^{x}}

\newline

x \sqrt{e^{x-1}}

\newline

\frac{1}{2 \sqrt{e^{x}}}

Posted 3 months ago

Question

What is the area of the region between the graphs of

f(x)=-x^{2}+2 x+12

g(x)=x^{2}-12

x=-3

x=4

\newline

1

\newline

7

\newline

\frac{343}{3}

\newline

\frac{83}{3}

\newline

\frac{52}{3} \sqrt{13}-1-32 \sqrt{3}

Posted 3 months ago

Question

What is the average value of

\frac{1}{x}

on the interval

4 \leq x \leq 8

\newline

1

\newline

\frac{3}{16}

\newline

\frac{1}{16}

\newline

\frac{\ln (32)}{4}

\newline

\frac{\ln (2)}{4}

Posted 3 months ago

Question

4

6

\newline

K

\newline

For the data given below, answer parts (a) through (f).

\newline

\begin{array}{cc}

\newline

x & y (\newline\)

-19

102

-16

122

-14

120

-13

132

-9

142

(\newline\)\end{array}

\newline

(a) Draw a scatter plot.

\newline

Choose the correct graph below.

\newline

\newline

\newline

\newline

\newline

(b) Find the equation of the line containing the first and the last data points.

\newline

y=4x+178

\newline

(Type an equation. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)

\newline

(c) Graph the line found in part (b) on the scatter plot.

\newline

Choose the correct graph below.

\newline

\newline

\newline

\newline

(d) Use a graphing utility to find the line of best fit.

\newline

y=\square x+\square

\newline

(Type integers or decimals rounded to four decimal places as needed)

Posted 2 months ago

Question

noot: Additional Practice (LMS graded)

\newline

2

\newline

e surface area of a paper cup is defined by the function

\newline

s(h)=6\pi\sqrt{16+h^{2}}

\newline

h

is the height of the cup. What is the domain and range of

\newline

s(h)

\newline

Describe the domain. Select the correct choice below and, if necessary, fill in the answer box within your choice.

\newline

A. The domain is

\newline

\{h\mid h>-\}

\newline

(Type an inequality or a compound inequality. Simplify your answer. Type an exact answer, using

\newline

\pi

\newline

B. The domain is all real numbers.

Posted 2 months ago

Question

Determine the coefficient and degree of the monomial.

\newline

-7x^{2}y^{5}

\newline

The coefficient of the monomial is

\newline

\square

\newline

The degree of the monomial is

\newline

\square

Posted 2 months ago

Question

\dfrac{a^2a^{-5}}{a^{-3}a^0}\cdot\left(\dfrac{a^2}{a^3}\right)^{-4}=a^x

Posted 2 months ago

Question

\frac{x}{3} + \frac{4x}{5} = \frac{1}{3}

Posted 2 months ago