Which of the following shows the domain of the following rational function?

\(f(x)=\dfrac{x + 3}{x^2 − x − 6}\)

Find the average rate of change of the function \(g(x)\) from \(x=2\) to \(x=4\).

\(g(x)=\dfrac{x}{x^2 − 1}\)

Find all the roots of the polynomial function:

\(p(x)=x^3−3x^2+4\)

The graph of \(p(x)=x^3\) is transformed to produce a new function \(q(x)\). The graph is shifted left 2 units, reflected over the x-axis, and shifted up 5 units. Which of the following represents \(q(x)\)?

The function \(f(x) = x^2 – 4x + 1\) is defined for all real numbers. Which of the following intervals has the greatest average rate of change of \(f(x)\)?

The function \(h(x)=x^2\) is moved horizontally by \(3\) units to the right, then stretched vertically by a factor of \(2\), and then moved vertically up by \(6\) units. Which of the below equations shows the function after the transformations?

A school district tracked the number of students enrolled in after-school programs over several years. The table below shows the data, where \(x\) represents years since 2015 and \(y\) represents the number of students enrolled.

Using a linear regression model, which equation best represents the data, and approximately how many students will be enrolled 10 years after 2015? (You may use a calculator.)

The graph below shows a polynomial function \(f(x)\). On which interval is \(f(x)\) increasing with a decreasing rate of change?

Find the zeros of the rational function:

\(r(x)=\dfrac{x^2−4x−12}{x^2−9}\)

Identify the polynomial from the graph shown below.

The population of lions in a sanctuary is equal to 2,060 in 2002. In 2007, the population of lions increased to 2,880. When will the population of lions reach 4,000?

(Assume a linear model for the question)

You may use a calculator.

Find the values of \(x\) for which the inequality \(6x^2−5x\) < \(x^3\) is true.

A polynomial \(p(x)\) has degree 10 with a positive leading coefficient. Which of the following statements about \(p(x)\) must be true?

A polynomial \(p(x)\) of degree 4 has real coefficients. If \(p(2)=−6\) and \(p(6)=1\), which statement must be true?

(Assume all roots are real and distinct.)

Which option shows the graph of the rational function \(\dfrac{1}{x − 6}\)?

Which of the below rational functions has \(\, y=2 \,\) as an asymptote?

Work out the vertical asymptotes for the function below:

\(f(x) = \dfrac{x − 3}{x^2 − 5x − 14}\)

Which line describes the end behavior asymptote for the function \(g(x)=\dfrac{x^4 − 16}{x^3 − 8}\)?

Work out the intervals on which:

\(\dfrac{1}{x} \lt \dfrac{2}{2x −9}\)

An environmental scientist is tracking the number of invasive fish in a lake over time. She notices that for the first several years, the population grows rapidly, but the growth begins to slow as the lake reaches capacity. Which type of function would best model this situation, and what feature of the data supports this choice?