Functions and Transformations Flashcards

Flashcards covering parent functions and transformation rules.

Linear Function

f(x) = x - A diagonal line.

Quadratic Function

f(x) = x^2 - A parabola.

Absolute Value Function

f(x) = |x| - A V-shape.

Cubic Function

f(x) = x^3 - An S-curve.

Square Root Function

f(x) = sqrt(x) - A half-curve.

Exponential Function

f(x) = b^x - Exhibits rapid growth or decay.

Logarithmic Function

f(x) = log_b(x) - The inverse of an exponential function.

Rational Function

f(x) = 1/x - Has two branches with asymptotes.

Vertical Shift

f(x) + k shifts the graph up, while f(x) - k shifts the graph down.

Horizontal Shift

f(x - h) shifts the graph right, while f(x + h) shifts the graph left.

Reflection over x-axis

-f(x) reflects the graph over the x-axis.

Reflection over y-axis

f(-x) reflects the graph over the y-axis.

Vertical Stretch/Compression

a*f(x) stretches the graph if |a| > 1 and compresses it if 0 < |a| < 1.

Horizontal Stretch/Compression

f(bx) compresses the graph if |b| > 1 and stretches it if 0 < |b| < 1.

Order of Transformations

Horizontal shift -> Stretch/compression/reflection -> Vertical shift.

Transformation of f(x) = |x| to g(x) = -2|x - 4| + 1

Reflect over the x-axis, stretch by 2, shift right 4 units, and shift up 1 unit.