Basic Functions Review

Basic Functions & Their Graphs

Linear Functions

• Slope-intercept form: $\boxed{y=mx+b}$
• 'm' is the slope
• 'b' is the y-intercept
• Slope-point form: $\boxed{y=m(x-x_0)+y_0}$
• 'm' is the slope
• (x0, y0) is a point on the line
• General form: $\boxed{\text{A}x~+~\text{B}y~+~C=0}$
• 'A' must be greater than 0
• Standard form: $\boxed{\text{A}x~+~\text{B}y=C}$
• 'A' must be greater than 0

Quadratic Functions

• Vertex Form: $\boxed{y=a(x-h)^2+k}$
• If a > 0, then y is a minimum
• If a < o, then y is a maximum
• (h, k) is the vertex
• x = h is the axis of symmetry
• Domain is $(-\infin,\infin)$
• Range is: $$
• $y\geq{k}~$ if a > 0
• $y\leq{k}~$ if a < 0

• General Form: $\boxed{x^2+\text{a}x+\text{b}y=\text{C}}$
• Standard Form: $\boxed{y=ax^2+bx+c}$

Cubic Functions

• Standard Form: $\boxed{y=ax^3+bx^2+cx+d}$

Reciprocal Functions

• $x\neq{0}$
• Vertical Asymptote at x = 0
• Horizontal Asymptote at y = 0
• Critical Points at (1, 1) & (-1, -1)

Radical Functions

Exponential Functions

• $b\neq{0}$
• Horizontal asymptote at y = 0

Logarithmic Functions

• $b\neq{0}$
• Vertical asymptote at x = 0