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Math 153 Exam #1 Study Guide

by: Sophia Valla

Math 153 Exam #1 Study Guide MATH 153

Marketplace > West Virginia University > Math > MATH 153 > Math 153 Exam 1 Study Guide
Sophia Valla
GPA 3.5

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About this Document

This is a breakdown of what to expect for the first exam
Calculus 1A with Precalculus
Andy Blankenship
Study Guide
Math, Calculus, Precalculus, Trigonometry
50 ?




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This 9 page Study Guide was uploaded by Sophia Valla on Tuesday September 6, 2016. The Study Guide belongs to MATH 153 at West Virginia University taught by Andy Blankenship in Fall 2016. Since its upload, it has received 21 views. For similar materials see Calculus 1A with Precalculus in Math at West Virginia University.

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Date Created: 09/06/16
Math 153 Exam #1 Study Guide Different Ways to Represent Functions ● There is only one X value for any Y value to pass the vertical line test ● Functions can be ordered pairs ● Functions must pass a vertical line test Evaluating Functions ● There is an x input which replaces an x in the function. The solution is the output  or the y value.      Finding Domains of Functions ● The domain for any polynomial is ALL REAL NUMBERS (-∞,∞) ● Almost all values in the domain  ○ ☆EXCEPTION ­ values that cause the denominator to be zero!! Radical Functions ● Can’t find EVEN ROOT of a NEGATIVE # ● Find domain of a radical that makes x positive Piecewise Functions ● Follows different rules at different intervals to uphold vertical line test ● OPEN dot = not included ● CLOSED dot = included ● When evaluating piecewise functions, apply the x value in f(x) to the  qualifications on the side to determine which function that x belongs to to get the proper  y value Composite Functions ● Where f ? g (x) = f(g(x)) and likewise?g f (x) = g(f(x)) ● Only time g ? f (x) = f? g (x) is when they are INVERSE FUNCTIONS of  each other so they equal X Inverse Functions ● (x,y) = (y,x) ●    F   =   F⁻¹ ● In order to solve inverse functions ○ Switch the x with y and solve for x Expression of a Cubic Function ● Ax³+bx²+cx+d ● f(5)= 80 , f(­3)= f(0) = f(6)=0 ○ Find a, b, c, d ○ All terms (EXCEPT d) disappear for f(0) ■ f(0)= a(0)³ + b(0)² + c(0) + d = 0 ● d=0 ○ ax³ + bx² + cx ■ f(5)= a(5)³ + b(5)² + c(5) = 80 ● 125a + 25b + 5c = 80 ■ f(­3)= a(­3)³ + b(­3)² + c(­3) =0 ● ­27a + 9b ­3c =0 ■ f(6)= a(6)³ + b(6)² + c(6) =0 ● 216a + 36b + 6c = 0 ○ System { 125a +25b +5c = 80 } { ­27a +9b ­3c = 0 } { 216a + 36b +6c = 0 }  ● Solve: a= ­2, b= 6, c= 36 ○ f(x)= ­2x³ +6x² +36x ● Or just use x intercepts (much easier way) Trigonometry Review ● x= adjacent  /  y= opposite  /  r= hypotenuse  ○ sin θ = y/r csc θ = r/y ○ cos θ = x/r sec θ = r/x ○ tan = y/x cot = x/y θ θ ● Use unit circle and special triangles and reference angles            Transformations of Functions and Graphs ● f(x) +h ○ Shift vertically ● f(x­h) ○ Shift horizontally ● f(ax) ○ Stretch or compress ● ­f(x) ○ Reflect across x­axis ● f(­x) ○ Reflect across y­axis Combination of Functions ● (f+g) (x) = f(x) + g(x) ● (f­g) (x) = f(x) ­ g(x) ● (fg) (x) = f(x) * g(x) ● (f/g) (x) = f(x) / g(x) Exponential Functions ● Laws  ● Graphs ○ Functions with a fraction slope are in DECLINE ○ Functions with a natural # slope are in INCLINE Natural Exponential Functions ● f(x) = e^x ○ a>1      →     e>1 ● Domain (-∞,∞) ● Range (0,∞) Logarithms                            ● Laws ○ Product  →logₐ(M)+logₐ(N)=logₐ(M+N) ○ Quotient  →logₐ(M)−logₐ(N)=logₐ(M/N) R ○ Power  M¿ =R∗logₐ(M) →logₐ¿ ● Natural Log (ln) ○ f(x) = ln(x) = logₑx ■ ln1=0 ■ lne=1


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