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Understanding Linear, Quadratic, Cubic, Exponential, and Power Functions

This article explores various types of mathematical functions including linear, quadratic, cubic, exponential, and power functions. Linear functions, represented as y = ax + b, exhibit a straight-line graph. Quadratic functions, denoted by y = ax² + bx + c, form a parabolic shape. Cubic functions, described by y = ax³ + bx² + cx + d, create a graph resembling an "S". Exponential functions, expressed as y = ab^x, feature a variable in the exponent. Power functions take the form y = ax^b and vary with the degree, offering diverse graphical representations.

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Understanding Linear, Quadratic, Cubic, Exponential, and Power Functions

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  1. 7.7

  2. Linear Function • y = ax + b OR y = mx + b • Linear functions just have a single x in the equation. • The graph of a linear function is a LINE.

  3. Linear Function

  4. Quadratic Function • y = ax2 + bx + c • Quadratic functions: • the highest degree is 2 (squared): x2 • The graph of a quadratic function is a parabola or “U”

  5. Quadratic Function

  6. Cubic Function • y = ax3 + bx2 + cx + d • Cubic Functions: • the highest degree is 3 (cubed): x3 • The graph of a cubic function is like an “S”.

  7. Cubic Function

  8. Exponential Function • y = abx • Exponential Function • The variable is in the exponent: abx • The graph of an exponential function is like a sideways parabola.

  9. Exponential Function

  10. Power Function • y = axb • Power Function • When you highest degree is different from a 2 (squared) or a 3 (cubed). • Graphs can differ in shape

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