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The Square Root Function

The Square Root Function. CPM Section 8.1. Graph the function of y = √x. No Sol. No Sol. 0 1 1.41 1.73 2. The Square Root Function. The general form of the square root function is y = d √x + e + f

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The Square Root Function

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  1. The Square Root Function CPM Section 8.1

  2. Graph the function of y = √x No Sol. No Sol. 0 1 1.41 1.73 2

  3. The Square Root Function • The general form of the square root function is y = d √x + e + f • A square root function is undefined when it is negative under the radical. • Thus the domain is…… • x + e ≥ 0, so x ≥ -e

  4. The Square Root Function • When x = -e, √x + e and y = f. • This point (-e,f) will either be a max or min value depending on whether the function is increasing or decreasing. This is determined by d. • If d>0 then the function is increasing. • If d<0 then the function is decreasing.

  5. The Square Root Function • Our range, then, • is y ≥ f if d > 0 • or y ≤ f if d < 0

  6. Domain?? • the domain is… x + e ≥ 0, so x ≥ -e • e = 3 • x + 3 ≥ 0 • x ≥ -3

  7. Increasing or decreasing? • If d>0 then the function is increasing. • If d<0 then the function is decreasing. • d = -2 • -2 < 0 • decreasing

  8. Min or Max and where is it?? • This point (-e,f) will either be a max or min value depending on whether the function is increasing or decreasing. This is determined by d. • d = -2, so d is negative • MAX • (-3,5)

  9. Range? • Our range is y ≥ f if d > 0 or y ≤ f if d < 0 • d = -2 therefore d < 0 • f = 5 • y ≤ 5

  10. Zero(s)? • Set y = 0 • 0 = • -5 = • (5/2) = • (5/2)2 = ( ) 2 • (25/4) = x + 3 • 13/4 = x

  11. Graph it!! 

  12. Domain • x ≥ 1 • Increasing or Decreasing • increasing • Max/Min and Where? • Min, (1,3) • Range? • y ≥ 3 • Zero(s) • x = 13/4 Graph it!!

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