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Unit 5. BASIC FUNCTIONS 23-24

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Transcript

Math

UNIT 5

BASIC FUNCTIONS

INDEX

  • 1) LINEAR FUNCTIONS
  • 2) QUADRATIC FUNCTIONS
  • 3) PIECEWISE FUNCTIONS
  • 4) ABSOLUTE VALUE FUNCTIONS
  • 5) RADICAL FUNCTIONS
  • 6)INVERSELY PROPORTIONAL FUNCTIONS
  • 7) EXPONENTIAL FUNCTIONS
  • 8) LOGARITHMIC FUNCTIONS

LINEAR FUNCTIONS

1.1. PROPORCIONALITY FUNCTIONS

  • The equation is y = mx
  • This equation passes through (0, 0)
  • m is called the slope
  • The slope is the coefficient of x when y is isolate.
    • If m > 0, the function is increasing
    • If m < 0, the function is decreasing

How graph a proporcionality function?

We make a table of values. You must choose aproppiate values

y=3x

y=x

y= -2x

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How graph a proporcionality function?

We make a table of values. You must choose aproppiate values

y=x/2

y= -4x

y= -3x/4

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1.2. LINEAR FUNCTIONS y = mx + n

  • The equation is y = mx +n
  • This equation passes through (0, n)
  • m is called the slope
  • n is called the Y-intercept
  • The slope is the coefficient of x when y is isolate
    • If m > 0, the function is increasing
    • If m < 0, the function is decreasing

How graph a linear function?

We make a table of values. You must choose aproppiate values

y = - 3x + 1

y = 2x - 4

y = x + 3

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How graph a linear function?

We make a table of values. You must choose aproppiate values

y = (x+3)/2

y = x/4 + 1

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1.3. CONSTANT FUNCTION y = n

m = 0. They are parallel to the X-axis

y = -4

y = 2

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QUADRATIC FUNCTIONS

QUADRATIC FUNCTIONS - Parabolas

  • Dom f(x) = IR
  • The general form is y = ax2 + bx + c
  • If a > 0, their branches point upwards. The parabola is happy
  • If a < 0, their brances point downwards. The parabola is sad

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How graph a quadratic function? y = ax2 + bx + c

- X-intercept: y = 0. Solve the equation ax2 + bx + c = 0 We get (x1, 0) and (x2, 0) - Y-intercept: x = 0. Substitute We get (0, c)

Table of values

Vertex

-b Vx = ----- 2a Vy = substitute in the parabola Vx

Calculate the value of the function at a few values close to the previous numbers.

Intercept with the axes

Examples

PIECEWISE FUNCTIONS

ABSOLUTE VALUE FUNCTIONS

RADICAL FUNCTIONS

INVERSELY PROPORTIONAL FUNCTIONS

EXPONENTIAL FUNCTIONS

EXPONENTIAL FUNCTIONS

  • The equation is y = ax
  • Expontential functions are continuous and the domain is R
  • Exponential functions passes through (0, 1) and (1,a)
    • If a > 1, the function is increasing
    • If 0 < a < 1, the function is decreasing

EXPONENTIAL FUNCTIONS

  • The equation is y = ax
  • Expontential functions are continuous and the domain is R
  • Exponential functions passes through (0, 1) and (1,a)
    • If a > 1, the function is increasing
    • If 0 < a < 1, the function is decreasing

How graph EXPONENTIAL FUNCTIONS?

y = 3x

y = (1/2)x

LOGARITHMIC FUNCTIONS

LOGARITHMIC FUNCTIONS

  • The logarithmic function is y = loga x , where a > 1
  • Dom f(x) = (0, inf)
  • Logartihmic function passes through (1, 0) and (a, 1)
    • If a > 1, the function is increasing
    • If 0 < a < 1, the function is decreasing

How graph LOGARITHMIC FUNCTIONS?

y = log 3 (x)

y = log 1/2 (x)

¡Gracias!