Consider the rational function $$m(x) = \frac{(x - 6)(x + 1)}{(x - 6)(x + 3)}$$. If the graph of $$m$$ has a hole, what is the $$y$$-coordinate of this hole?

For the piecewise function given above, solve for x in the equation when the function equals the specified value: solve $$2*x+1 = 7$$ for $$x<3$$ and $$x^2-4*x+3 = 0$$ for $$x \ge 3$$, then determine the valid solution.

What does it mean if a function has no zeros?

The binomial theorem can be used to expand the polynomial function $$u$$, given by $$u(x) = (3x + 4)^4$$. What is the coefficient of the $$x^2$$ term in the expanded polynomial?

Evaluate the transformed quadratic function $$f(x)=(x-2)^2$$ at $$x=5$$.

A ball is thrown upward from a height of 6 feet with an initial velocity of 32 feet per second. The height decreases at an increasing rate after reaching its maximum. Which function type would be most appropriate to model the height h(t) after t seconds?

The rational function $$f(x) = \frac{(x + 4)(x - 2)}{(x + 4)(x + 1)}$$ has a hole in its graph. After removing the hole, what is the simplified form of $$f(x)$$?

The table above represents a polynomial function $$h(x)$$ with equally spaced x-values. Determine the degree of the polynomial by examining its finite differences.

For a quadratic function, how do the average rates of change over consecutive equal-length intervals behave?

Consider the rational function $$r(x) = \frac{(x - 3)(x - 11)}{(x - 3)(x + 1)}$$. At what value of $$x$$ does the graph of $$r$$ have a hole, and what is the limit of $$r(x)$$ as $$x$$ approaches this value?

Which of the following is true regarding the vertical asymptote and/or hole for the rational function $$r(x)=\frac{x-2}{(x-2)^2}$$?

Using the binomial theorem to expand $$(2x + 3)^4$$, what is the coefficient of the $$x^2$$ term?

Which of the following statements is true?

Solve the equation $$ (x+2)^2 = 16$$.

Which of the following describes a concave up quadratic function?

The table gives values for a polynomial function $$f$$ at selected values of $$x$$. What is the average rate of change of $$f$$ over the closed interval $$[1,4]$$?

Without a calculator: An exponential function is known to be increasing with a horizontal asymptote at y = 0 and satisfies f(0) = 2. The table shows that f(1) = 3 and f(2) = 4.5. Which equation correctly represents this function?

The polynomial function $$f(x) = x^4 - 8x^3 + 24x^2 - 32x + 16$$ has a zero at $$x = 2$$. What is the multiplicity of this zero?

If $$a < b$$, then $$g(a) > g(b)$$ for all $$a$$ and $$b$$ in the interval $$3 < x < 7$$. Which of the following could be true about the graph of $$g$$ on the interval $$3 < x < 7$$?

Consider the function $$f(x)= x^4 - 2*x^2+1$$. Is this function even, odd, or neither?