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F(x) terminology

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F(x) terminology

1. 1. F(X) TERMINOLOGY SECTION 4.4 September 20/21, 2010
2. 2. ACT Opener <ul><li>Solve 2x + 6 – 5x < 15 </li></ul><ul><li>A. x < -3 </li></ul><ul><li>B. x > -3 </li></ul><ul><li>C. x < 3 </li></ul><ul><li>D. x > 3 </li></ul><ul><li>E. x = -3 </li></ul><ul><li>Solve 7x – 3 > 5x -7 </li></ul><ul><ul><li>x > -7 </li></ul></ul><ul><ul><li>x < 5 </li></ul></ul><ul><ul><li>x > -2 </li></ul></ul><ul><ul><li>x < -3 </li></ul></ul><ul><ul><li>x = -7 </li></ul></ul><ul><li>Solve the system using Cramer’s Rule. </li></ul><ul><ul><li>5x – 8y = -10 </li></ul></ul><ul><ul><li>6x + 12y = 6 </li></ul></ul>
3. 3. f(x) Terminology <ul><li>f(x) </li></ul><ul><ul><li>It is pronounced “f of x” </li></ul></ul><ul><ul><li>It means “the value of y in function f , where the independent variable is x. ” </li></ul></ul><ul><ul><li>Any letter may be used for the name of a function </li></ul></ul><ul><ul><li>f(x) terminology allows us to show what value is being substituted for x . </li></ul></ul>
4. 4. f(x) Terminology <ul><li>y = -7x + 100 </li></ul><ul><li>f(x) = -7x + 100 </li></ul>Function name Variable used in function
5. 5. Examples: Let f(x) = -7x+100 <ul><li>f(  ) </li></ul><ul><li>f(  ) = -7(  ) + 100 </li></ul><ul><li>f(7) </li></ul><ul><li>f(7) = -7(7) + 100 </li></ul><ul><li>f(7) = -49 + 100 </li></ul><ul><li>f(7) = 51 </li></ul>
6. 6. Examples: Let f(x) = x + 25 and g(x) = x 2 – 5x <ul><li>f(f(6)) </li></ul><ul><li>= f( (6)+25 ) </li></ul><ul><li>= f( 31) </li></ul><ul><li>= (31) + 25 </li></ul><ul><li>= 56 </li></ul>Pronounced “f of f of 6”
7. 7. Examples: Let f(x) = x + 25 and g(x) = x 2 – 5x <ul><li>f(g(1)) </li></ul><ul><li>=f((1) 2 – 5(1)) </li></ul><ul><li>=f(1 - 5) </li></ul><ul><li>=f(-4) </li></ul><ul><li>= (-4) + 25 </li></ul><ul><li>=21 </li></ul><ul><li>f(q) </li></ul><ul><li>f(q) = q + 25 </li></ul><ul><li>f(g(k)) </li></ul><ul><li>= f((k) 2 – 5(k)) </li></ul><ul><li>= f(k 2 – 5k) </li></ul><ul><li>= (k 2 – 5k)+25 </li></ul><ul><ul><li>= k 2 – 5k+25 </li></ul></ul>
8. 8. Examples: Let f(x) = x + 25 and g(x) = x 2 – 5x <ul><li>g(f(L)) </li></ul><ul><li>= g(L + 25) </li></ul><ul><li>= (L + 25) 2 – 5(L + 25) </li></ul><ul><li>= (L + 25)(L + 25) – 5L – (5)(25) </li></ul><ul><li>= L 2 + 50L + 625 – 5L – 125 </li></ul><ul><li>= L 2 + 45L + 500 </li></ul>
9. 9. Examples <ul><li>Page 131 #28 </li></ul><ul><li>t = number of minutes since they left boatdock </li></ul><ul><li>f(t) = number of meters they are away from boatdock on the way out </li></ul><ul><li>g(t) = number of meters they are away from boatdock on the way back in </li></ul>
10. 10. Page 131 #28 <ul><li>f(t) = 32t </li></ul><ul><li>f(3) f(7) f(10) </li></ul><ul><li>f(3) = 32(3) f(7) = 32(7) f(10) = 32(10) </li></ul><ul><li>f(3) = 96 f(7) = 224 f(10) = 320 </li></ul><ul><li>g(t) = -17t + 510 </li></ul><ul><li>g(18) g(23) </li></ul><ul><li>g(18) = -17(18) + 510 g(23) = -17(23) + 510 </li></ul><ul><li>g(18) = 204 g(23) = 119 </li></ul>
11. 11. Page 131 #28 <ul><li>C.) </li></ul>10 20 30 t 100 200 300 400 f(t) or g(t) g f (10.41, 333.12)
12. 12. Page 131 #28 <ul><li>D.) f(t) = g(t) </li></ul><ul><li>32t = -17t + 510 </li></ul><ul><li>+17t + 17t </li></ul><ul><li>49t = 510 </li></ul><ul><li>49 49 </li></ul><ul><li>t = 10.41 minutes </li></ul><ul><li>f(10.41) = 32(10.41) </li></ul><ul><li>f(10.41) = 333.12 meters </li></ul><ul><li>E) At the point where the graphs intersect, the boat was turning around. </li></ul>
13. 13. Page 131 #28 <ul><li>F) g(t) = 0 </li></ul><ul><li>0 = -17t + 510 </li></ul><ul><li>-510 -510 </li></ul><ul><li>-510 = -17t </li></ul><ul><li>-17 -17 </li></ul><ul><li>t = 30 minutes </li></ul>
14. 14. Exit Slip <ul><li>Let f(x) = 3x + 11 and g(x) = x 2 + x + 1 </li></ul><ul><li>Evaluate the following: </li></ul><ul><li>f(-5) </li></ul><ul><li>g(f(-5)) </li></ul>
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