You will need: calculator Date: 1.4 Notes: Functions   Lesson Objective: Use function notation to evaluate and find the domain of functions, and solve real-life problems You will need: calculator Real-World App: Will a baseball clear a 10-foot fence located 300 feet from home plate? This is Jeopardy!!!: This is f(4 + h) when f(x) = x² – 2x + 9.

Lesson 1: Definition of Function and the Function Notation Function Notation: “f” Input Output Equation x f(x) f(x) = x² + 1

f(t) = 3 𝑡+4 Lesson 2: The Domain of a Function Find the domain of each function. f(x) = 3x – 4 s(y) = 3𝑦 𝑦−6 f(x) = 𝑥 − 5 𝑥² −9 f(t) = 3 𝑡+4

Lesson 3: The Path of a Baseball A baseball is hit a point 3 feet above the ground at a velocity of 100 feet per second and an angle of 45°. The path of the baseball is given by y = -0.0032x² + x + 3, where x and y are measured in feet. Will the baseball clear a 10-foot fence located 300 feet from home plate?

Lesson 3: The Path of a Baseball Will the baseball clear a 10-foot fence located 300 feet from home plate? y = -0.0032x² + x + 3 

Lesson 4: Piecewise-Defined Function The number V (in thousands) of alternative-fueled vehicles in the U.S. increased in a linear pattern from 1995 to 1999. Then in 2000, the number of vehicles took a jump and, until 2002, increased in a different linear pattern as shown on the next slide, where t represents the year with t = 5 corresponding to 1995. Use this function to approximate the number of alternative-fueled vehicles for each year from 1995 to 2002.

Lesson 4: Piecewise-Defined Function Use this function to approximate the number of alternative-fueled vehicles for each year from 1995 to 2002. V(t) = 18.08𝑡+155.3, 5≤𝑡≤9 38.20𝑡+10.2, 10≤𝑡≤12

Lesson 5: Difference Quotients For f(x) = x² – 2x + 9, find the difference quotient 𝑓 4+ℎ −𝑓(4) ℎ , h ≠ 0.

Lesson 6: Re-writing Functions For a cone, the ratio of its height to its radius is 3. Express the volume of a cone, V = 1 3 π𝑟²ℎ as a function of the radius, r.

Lesson 7: Applying Geometry to Algebra A rectangle is bounded by the x-axis and the Semicircle y = 36− 𝑥 2 (see figure). Write the area of the rectangle as a function of x, and determine the domain of the function.

Find the domain of each function. 1.4: DIGI Yes or No Find the domain of each function. f: {(-3, 0), (-1, 4), (0, 2), (2, 2), (4, -1)} g(x) = 3𝑦 𝑦+5 3. h(x) = 4−𝑥² 4. Using the same info from Lesson 3, will the base-ball clear a 20’ fence located 280’ from home plate? For f(x) = x² – 4x + 7, find the difference quotient 𝑓 𝑥+ℎ −𝑓(𝑥) ℎ , h ≠ 0. 6. The ratio of the height of an experimental can to its radius is 4. Write the volume of the can as a function of the radius, r. Then write the function in terms of height, h.

Lesson 2: Piecewise-Defined Function Evaluate the function. f(x) = 3𝑥 −4, 𝑥<0 3𝑥+1, 𝑥≥0 when x = -2, 0, and 2