If the secant line through points (1, f(1)) and (4, f(4)) on the graph of f(x) = mx² + nx has slope 22, and the secant line through (1, f(1)) and (3, f(3)) has slope 14, what is the value of m?

What does a larger average rate of change indicate about a function over an interval?

The rational function $$f(x) = \frac{(x^2 - 9)(x + 5)}{(x^2 - 9)(x - 1)}$$ has holes in its graph. What are the coordinates of the hole that occurs at $$x = 3$$?

What is the primary purpose of using polynomial long division in the context of rational functions?

A researcher collected data points and calculated the following: First differences increase steadily, second differences are approximately 8.2 across all calculations, third differences vary. Which statement best describes the appropriate model?

If the function $$f(x) = 3x + 2$$, what is the input-output pair for its inverse when the output is 5?

The function $$g(x)= \log_{5}(x-3)$$ models a reaction rate. What is the domain of $$g(x)$$?

A town's population is modeled by P(t) = 12000(1.03)^t, where t is the number of years since 2020. The base 1.03 in this model indicates that the population:

If a^(1/n) = b^(1/m) where a, b > 0 and m, n are natural numbers, which of the following must be true?

How does the power property affect the graph of $$f(x) = \log_b(x^k)$$?

A car's position function $$s(t) = 3t^2 - 2t + 5$$ represents its distance in miles from a starting point after $$t$$ hours. To determine when the rate of change is positive, you calculate the average rate of change over small intervals near $$t = 1$$. Which intervals would best approximate the instantaneous rate of change at $$t = 1$$?

Which of the following rational functions will NOT have a horizontal asymptote at y = 0?

A company's profit P(x) in thousands of dollars is modeled by $$P(x) = -2x^2 + 16x - 24$$, where x is the number of products sold in hundreds. Which assumption is most critical for this quadratic model?

The second difference of a function's values represents the rate at which the average rates of change are changing. What is the second difference for f(x) = 5x - 9 when evaluated at equally spaced x-values with increment 1?

Evaluate the polynomial function $$f(x)=x^3+2*x^2-5*x+1$$ at $$x=-1$$.

A company's profit $$P$$ (in thousands of dollars) depends on the number of units $$x$$ produced daily. When no units are produced, the company loses $$\$50,000$$ due to fixed costs. The profit reaches its maximum of $$\$100,000$$ when 200 units are produced, then decreases. Which quadratic model best represents this scenario?

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 $$f(x)$$?

If p(x) = x⁵ + ax⁴ + bx³ + cx² + dx + e has zeros at 1, 2, and 3 - 2i, where a, b, c, d, and e are real numbers, which of the following statements is true?

A company's profit depends on the number of products sold. The profit starts at $$-\$5000$$ (initial loss), increases to a maximum around 500 units sold, then decreases due to production constraints. Which function type best models this scenario?

What is the primary characteristic of a quadratic regression model?