Flashcard Parent Functions and Transformations

The parent absolute value function is defined as $$f(x) = |x|$$ , which produces a V-shaped graph that opens upwards.

Reflecting the absolute value function vertically changes the function to $$f(x) = -|x|$$ , flipping the graph upside down.

To shift the parent absolute value function to the right by 15 units, the equation becomes $$f(x) = |x - 15|$$ .

Shifting a function down by 3 units means subtracting 3 from the function's output, resulting in $$f(x) = |x| - 3$$ for the absolute value function.

The parent square root function is defined as $$f(x) = \text{sqrt}(x)$$ .

The transformations include a vertical reflection, a vertical shrink by a factor of 1/2, a shift right by 5 units, and a shift up by 3 units.

A vertical stretch occurs when the output of a function is multiplied by a factor greater than 1, making the graph taller.

Reflecting a function over the x-axis means multiplying the function's output by -1, resulting in $$f(x) = -g(x)$$ .

The parent cubic function is defined as $$f(x) = x^3$$ , which produces an S-shaped graph.

To identify the parent function, look for the basic form of the function before any transformations are applied.