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Common Parent Functions

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(1)

Linear Function:

f(x) = x

Domain: All real numbers Range: All real numbers X – Intercept: (0, 0) Y – Intercept: (0, 0)

Quadratic Function:

f(x) = x

2

Domain: All real numbers Range: y ≥ 0

X – Intercept: (0, 0) Y – Intercept: (0, 0)

(2)

Cubic Function:

f(x) = x

3

Domain: All real numbers Range: All real numbers X – Intercept: (0, 0) Y – Intercept: (0, 0)

Absolute Value Function:

f(x) = |x|

Domain: All real numbers Range: y ≥ 0

X – Intercept: (0, 0) Y – Intercept: (0, 0)

(3)

Square Root Function:

f(x) =

√𝒙

Domain: x ≥ 0 Range: y ≥ 0 X – Intercept: (0, 0) Y – Intercept: (0, 0) Reciprocal Function:

f(x) =

𝟏

𝐱

Domain: All real numbers; x ≠ 0 Range: All real numbers; y ≠ 0 X – Intercept: Does not exist Y – Intercept: Does not exist Horizontal asymptote at y = 0

(4)

Natural Exponential Function:

f(x) = e

x

Domain: All real numbers Range: y > 0

X-Intercept: Does not exist Y-Intercept: (0, 1)

Horizontal asymptote at y = 0

Natural Logarithmic Function:

f(x) = lnx

Domain: x > 0

Range: All real numbers X-Intercept: (1, 0)

Y-Intercept: Does not exist Vertical asymptote at x = 0

(5)

Sine Function:

f(x) = sin x

Domain: All real numbers Range: -1 ≤ x ≤ 1

X – Intercept: kπ, where k is an integer Y – Intercept: 0

Period: Amplitude: 1

(6)

Tangent Function:

f(x) = tan x

Domain: All real numbers except π/2 + k, where k is an integer Range: All real numbers

X-Intercept: (kπ, 0) where k is an integer Y-Intercept: (0, 0)

Period: π

Amplitude: Does not exist

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