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Parent Functions

Parent Functions. General Forms Transforming linear and quadratic function. Linear Function. Has a momma equation: y=x This graph can shift up, down, right, left, or get steeper or flatter. Linear Function. f(x)=x. X intercept: Y intercept: Slope:. Linear Function. f(x)=x

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Parent Functions

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  1. Parent Functions General Forms Transforming linear and quadratic function

  2. Linear Function • Has a momma equation: y=x • This graph can shift up, down, right, left, or get steeper or flatter

  3. Linear Function • f(x)=x X intercept: Y intercept: Slope:

  4. Linear Function • f(x)=x • Domain: all real numbers • Range: all real numbers

  5. Transformations Linear and Quadratic

  6. Vertical Shifts • The y intercept changes • F(x) changes to f(x)=x+k • If k is greater than 0 the intercept moves up k units • If k is less than 0, the intercept moves down k units • http://merganser.math.gvsu.edu/m221/transform/linear.html

  7. Horizontal Shift • The input value changes • F(x) changes to f(x+h) • Wherever there was an x in the equation it is now replaced with x+h

  8. Horizontal Shifts • If h is greater than 0, shift is to the left • If h is less than 0, shift is to the right • Opposite of what you would think

  9. Reflection across y axis • The input value changes • F(x) changes to f(-x) • Lines are symmetric about the y axis

  10. Reflection across the x axis • The slope of the line changes signs • F(x) changes to –f(x) • Looks exactly like a reflection across the y axis for a linear function

  11. Changing the steepness • The number in front of the x is larger than 1- slope is larger, line is steeper • The number in front of the x is smaller than 1- the slope is smaller, the line is flatter

  12. Example • Describe the change in the original equation • F(x)=2x+3 • Momma equation was: • We have now…. • TI Smart View

  13. Checking on the Calculator • In y1 put x • In y2 put the new function • Look at the difference

  14. Try Another • Sketch the new graph/Describe the changes • F(x)=3(x+1)+4

  15. Another • Write the equation describing the shift • The momma equation is f(x)=x. There is a vertical shift down by 2 and the slope is increased by 5

  16. Another • How would I change the previous problem to include a shift to the left of 2?

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