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F(x) terminology

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This document contains terminology and examples related to functions. It defines f(x) as "the value of y in function f, where the independent variable is x". It provides examples of evaluating functions like f(x) = -7x + 100 for different x values. It also gives examples of composite functions like f(f(x)) and using different functions like f(x) and g(x) together. The examples relate to word problems about distances over time on a boat trip.

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

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F(x) terminology

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