1 / 12

Operations with Functions: Add, Subtract, Multiply, & Divide

Explore examples of adding, subtracting, multiplying, and dividing functions. Learn how different functions interact and simplify your calculations.

lebeau
Télécharger la présentation

Operations with Functions: Add, Subtract, Multiply, & Divide

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. a. f(x) + g(x) f(x) – g(x) b. EXAMPLE 1 Add and subtract functions Letf (x)= 4x1/2andg(x)=–9x1/2. Find the following. SOLUTION f (x) + g(x) = 4x1/2 + (–9x1/2) = [4 + (–9)]x1/2 = –5x1/2 SOLUTION f (x) – g(x) = [4 – (–9)]x1/2 = 13x1/2 = 4x1/2 – (–9x1/2)

  2. The functions fand geach have the same domain: all nonnegative real numbers. So, the domains of f + gand f – galso consist of all nonnegative real numbers. c. the domains of f + gand f – g EXAMPLE 1 Add and subtract functions SOLUTION

  3. a. f (x) g(x) b. 6x f (x) f (x) g(x) g(x) x3/4 f (x) g(x) = = 6x1/4 = 6x(1 – 3/4) EXAMPLE 2 Multiply and divide functions Let f (x)= 6xand g(x) = x3/4. Find the following. SOLUTION = (6x)(x3/4) = 6x(1 + 3/4) = 6x7/4 SOLUTION

  4. The domain of f consists of all real numbers, and the domain of gconsists of all nonnegative real numbers. So, the domain of f gconsists of all nonnegative real numbers. Because g(0) = 0, the domain of is restricted to all positive real numbers. f g EXAMPLE 2 Multiply and divide functions f g and the domains of f c. g SOLUTION

  5. r(m) s(m) (6 106)m0.2 = 241m–0.25 = • Findr(m) s(m). EXAMPLE 3 Solve a multi-step problem Rhinos For a white rhino, heart rate r(in beats per minute) and life span s(in minutes) are related to body mass m(in kilograms) by these functions: • Explain what this product represents.

  6. Find and simplify r(m) s(m). r(m) s(m) = 241m –0.25 [ (6 106)m0.2 ] 241(6 106)m(–0.25 + 0.2) = (1446 106)m –0.05 = (1.446 109)m –0.05 = EXAMPLE 3 Solve a multi-step problem SOLUTION STEP 1 Write product of r(m) and s(m). Product of powers property Simplify. Use scientific notation.

  7. Interpret r(m) s(m). EXAMPLE 3 Solve a multi-step problem STEP 2 Multiplying heart rate by life span gives the total number of heartbeats for a white rhino over its entire lifetime.

  8. f (x) + g(x) f (x) – g(x) for Examples 1, 2, and 3 GUIDED PRACTICE Let f (x) = –2x2/3andg(x) = 7x2/3. Find the following. SOLUTION f (x) + g(x) = –2x2/3 + 7x2/3 = 5x2/3 = (–2 + 7)x2/3 SOLUTION f (x) – g(x) = –2x2/3 – 7x2/3 = [–2 + ( –7)]x2/3 = –9x2/3

  9. the domains of f + gand f – g for Examples 1, 2, and 3 GUIDED PRACTICE SOLUTION all real numbers; all real numbers

  10. f (x) g(x) f (x) g(x) for Examples 1, 2, and 3 GUIDED PRACTICE Let f (x) = 3xandg(x) = x1/5. Find the following. SOLUTION 3x6/5 SOLUTION 3x4/5

  11. the domains off g and f g for Examples 1, 2, and 3 GUIDED PRACTICE SOLUTION all real numbers; all real numbers except x=0.

  12. Use the result of Example 3 to find a white rhino’s number of heartbeats over its lifetime if its body mass is 1.7 105kilograms. about 7.92 108 heartbeats for Examples 1, 2, and 3 GUIDED PRACTICE Rhinos SOLUTION

More Related