Graphs of Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the value of a function at a specific point?

Back

To find the value of a function g(x) at a specific point x = a, substitute a into the function: g(a).

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is f(x) = x^2. It is a parabola that opens upwards.

Front

What transformation occurs when a function is shifted down by 6 units?

Back

When a function f(x) is transformed to g(x) = f(x) - 6, the entire graph of the function is shifted down 6 units.

Front

What is the general form of a cubic function?

Back

The general form of a cubic function is f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

What is an exponential function?

Back

An exponential function is a function of the form f(x) = ab^x, where a is a constant, b is a positive real number, and b ≠ 1.

Front

How do you identify a square root function?

Back

A square root function has the form f(x) = √x or f(x) = a√(x - h) + k, where (h, k) is the vertex of the graph.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function graphs as a straight line and has a degree of 1, while a quadratic function graphs as a parabola and has a degree of 2.

Front

What does the graph of a cube function look like?

Back

The graph of a cube function, f(x) = x^3, has an S-shape and passes through the origin, with one end going to positive infinity and the other to negative infinity.

Front

What is the significance of the y-intercept in a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the value of the function when x = 0.