M348 Transformations of FUNctions

Front

What is the general form of a cubic function?

Back

f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

What transformation is represented by g(x) = (x - 1)^3?

Back

The function g(x) is a horizontal shift of the original function f(x) = x^3 to the right by 1 unit.

Front

How does reflecting a function over the y-axis affect its equation?

Back

Reflecting a function over the y-axis changes f(x) to f(-x).

Front

What does the transformation g(x) = |-x + 3| indicate?

Back

This transformation involves reflecting the function over the y-axis and shifting it left by 3 units.

Front

What is the effect of a negative sign in front of a function, such as g(x) = -f(x)?

Back

It reflects the function over the x-axis.

Front

Describe the transformation from f(x) = x^2 to g(x) = -(x + 5)^2.

Back

The transformation involves shifting the graph left by 5 units and reflecting it over the x-axis.

Front

What does the transformation g(x) = -g(x + 6) - 10 entail?

Back

This transformation reflects the function over the x-axis, shifts it down by 10 units, and shifts it left by 6 units.

Front

If f(x) = x^2, what is the effect of changing it to f(x) = (x + c)^2?

Back

This transformation shifts the graph of the function horizontally to the left by c units if c is positive, and to the right if c is negative.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the highest or lowest point of the parabola, depending on the direction it opens.

Front

How do you determine the direction of a parabola from its equation?

Back

If the coefficient of x^2 is positive, the parabola opens upwards; if negative, it opens downwards.