A function is defined as a relationship where each input has exactly one output. What is the general form of a linear function?

The general form of a linear function is f(x) = mx + c, where m is the slope and c is the y-intercept.

Fill in the blank: The domain of a quadratic function f(x) = ax² + q is ___ and the range depends on the value of a.

X ∈ ℝ

True or False: The graph of y = ax² opens downwards when a > 0.

False. The graph opens downwards when a <>

What point on the graph of the quadratic function f(x) = x² represents the vertex?

The vertex is at the point (0, 0).

Riddle: I have a slope and a y-intercept, my graph is a straight line. What am I?

A linear function.

What is the range of the quadratic function y = ax² + q when a > 0?

The range is y ≥ q.

Fill in the blank: The function y = abˣ has a horizontal asymptote at ___ when b > 1.

Y = 0

Identify the intercepts of the function f(x) = x². What are the x- and y-intercepts?

The x-intercepts are (0, 0), and the y-intercept is also (0, 0).

True or False: A hyperbola has vertical and horizontal asymptotes at x = 0 and y = 0.

True.

What is the general shape of the graph for a quadratic function?

The graph of a quadratic function is a parabola.

Riddle: I can increase rapidly as my input grows, and I always remain positive. What am I?

An exponential function.

Fill in the blank: The function notation for a function is typically represented as ___.

F(x)

What is the significance of the turning point in a quadratic function?

The turning point, or vertex, is where the function changes direction.

How can you determine the domain of the hyperbolic function y = a/x?

The domain is all real numbers except x = 0.

True or False: The range of the exponential function y = abˣ is all real numbers.

False. The range is y > 0 for b > 1.

What defines the asymptotes of the hyperbola represented by the equation y = a/x?

The asymptotes are the lines x = 0 and y = 0.

What is the effect of the value q in the quadratic function f(x) = ax² + q?

The value q shifts the graph vertically; if q > 0, it shifts upward, and if q < 0,="" it="" shifts="">

Riddle: I describe a set of all possible output values for a function. What am I?

The range.

What is meant by the term 'asymptote' in graphing functions?

An asymptote is a line that the graph approaches but never intersects.

What defines a function in terms of its inputs and outputs?

A function is a relationship where each input has exactly one output.