Precalculus ­ 1.7 ­ Variation & Applications

1

January 05, 2017

3.6 #15­39odd Solving polynomial inequalities#47, 53­61odd Solving rational inequalities

3.7: #23­37 odd Variation4.1 #17‐23 odd prove f is one‐to‐one; prove g is not one­to‐one

#59‐63 odd determine if f is on‐to‐one and if so, determine its inverse #77‐81 odd sketch the inverse function by reflecting over y=x

#83‐87 odd use composition to show that the functions are inverses

4.2 #5‐10all match an exponential function to its graph #11‐41odd sketch graphs of exponential functions using transformations#43a,b,c,45,47 compound interest word problems

4.3 #1‐8all sketch graphs of logarithmic functions#9‐33odd evaluate log expressions without a calculator#35‐53 odd convert between logarithmic and exponential expressions#69‐77 odd apply change of base formula & calculator to approximate log expressions#83‐90 all graph logarithmic functions using transformations

Precalculus ­ 1.7 ­ Variation & Applications

2

January 05, 2017

Solve the inequality:

Given the line 2x­3y=5, determine the equations of both a line parallel to and perpendicular to this line which pass through the point (1,1).

Precalculus ­ 1.7 ­ Variation & Applications

3

January 05, 2017

Kent Murdick's trick for graphing polynomials without rational zeros(http://youtu.be/NBngJjQ6LBg)

y=x3+5x2+3

3.7 Variation and Applications

2­variable direct variation ­­ "y varies directly with x"y=kx , k=constant of variation

inverse/indirect variation ­­ "y varies inversely with x"

8. Find the variation constant and write an equation of variation ify varies directly as x, and y=3 when x=33.

Precalculus ­ 1.7 ­ Variation & Applications

4

January 05, 2017

4. Find the variation constant and write an equation of variation ify varies inversely with x, and y=12 when x=5.

34. Find the variation constant and write an equation of variation if y varies jointly as x and z and inversely as the square of w.y=12/5 when x=16, z=3, and w=5.

*joint variation is direct variation with more than one variable

Precalculus ­ 1.7 ­ Variation & Applications

5

January 05, 2017

22. The f­stop of a 23.5 mm­diameter lens is directly proportional to the focal length F of the lens. If a 150­mm focal length corresponds to an f­stop of 6.3, find the f­stop of a 23.5 mm diameter lens with a focal length of 80 mm.

38. The weight W of an object varies inversely as the square of the distance d from the center of the earth. At sea level (3978 mi from the center of the earth), an astronaut weighs 220 lb. Find his weight when he is 200 mi above the surface of the earth.