csp 100- basic function graphs & transformations

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graph for y=x

linear function with a slope of 1, passing through the origin.

graph for x²

a parabolic graph that opens upwards, with its vertex at the origin and axis of symmetry along the y-axis.

graph for x³

a cubic function graph that passes through the origin, exhibiting symmetry about the origin and having an inflection point at the origin.

graph for lxl

V-shaped graph that opens upwards, with its vertex at the origin and axis of symmetry along the y-axis.

graph for square root of x

a curve that starts at the origin and rises gradually to the right.

graph for cubed root of x

a curve that passes through the origin, rising gradually to the right.

f(x) + c

a shift of f(x) c units up > add c to all y-values

f(x) - c

a shift of f(x) c units down > subtract c to all y-values

f(x-c)

a horizontal shift of f(x) c units to the right > add c to all x-values

f(x+c)

a horizontal shift of f(x) c units to the left > subtract c from all x-values

-f(x)

a vertical reflection of f(x) across the x-axis > multiply all y-values by -1

f(-x)

a horizontal reflection of f(x) across the y-axis > multiply all x-values by -1

cf(x)

a vertical stretch or compression of f(x) by a factor of c > multiply all y-values by c

f(cx)

a horizontal stretch or compression of f(x) by a factor of 1/c > multiply all x-values by 1/c