12 Basic Functions Flashcards

Question

Describe the graph and equation of: ***The Reciprocal Function*** Domain and range? Even or odd? Continuous? One-to-One? Inverse of another basic function? Asymptotes?

Answer 1

Diagonal hyperbola: f(x)= 1/x ## Footnote Domain: x≠0 Range y≠0 Odd NOT Continuous One-to-one Not an inverse Asymptotes at both axes

Answer 2

Sideways half-parabola: f(x)=√x ## Footnote Domain: [0, +∞) Range: [0, +∞) Neither even nor odd Continuous One-to-one Inverse of squaring function No asymptotes

Answer 3

J-shape: f(x)=e^x ## Footnote Domain: AR# Range: (0, +∞) Neither even nor odd Continuous One-to-one Not an inverse Asymptote on x-axis (y=0)

Answer 4

Curve facing down/left: f(x)=ln(x) ## Footnote Domain: (0, +∞) Range: AR# Neither even nor odd Continuous One-to-one Not an inverse Asymptote @ y-axis (x=0)

Answer 5

Horizontal squiggle: f(x)=sin(x) ## Footnote Domain: AR# Range: [-1, 1] Odd Continuous Not one to one Not an inverse No asymptotes

Answer 6

Hoziontal squiggle: f(x)= cos(x) Domain: AR# Range: [-1, 1] Even Continuous Not one-to-one Not an inverse No asymptotes

Answer 7

Large V: f(x)=|x| (aka abs(x) ## Footnote Domain: AR# Range [0, +∞) Even Continuous Not one-to-one Not an inverse No asymptotes nb Min. point= Cusp

Answer 8

Steps increasing left-\>right: f(x)=int x int x=largest whole number ≤ x Domain: AR# Range: All integers Neither even nor odd NOT Continuous Not one-to-one Not an inverse No asymptotes nb aka Piecewise/step function

Answer 9

Increase then plateau: f(x)= 1/(1+e^-x) Domain: AR# Range: (0, 1) Neither even nor odd Continuous One-to-one Not an inverse Asymptotes @ x-axis (y=0) and y=1

Answer 10

A limit is another word for an asymptote which gives more information by indicating from which direction the function approaches it. Becaues the ***reciprocal function*** approaches its x-axis asymptote as x increases to the right, it would have a limit of f(x)=0 as x→+∞ Because the ***logistic function*** approaches its asymptote at y=1 as x increases from left to right, it would have a limit of f(x)=1 as x→+∞ Because the ***exponential function*** approaches its asymptote on the x-axis as x decreases to the left, it would have a limit at f(x)=0 as x→**-∞**

Answer 11

Plug 0 in for y to find the x-intercepts and plug 0 into x to find the y intercepts. The equation for the natural logarithm function is y=ln(x). Due to its vertical asymptote at the y-axis it has no y-intercept, but to find its x-intercept I will plug 0 in for y 0=ln(x) e⁰=x ***1=x***

Answer 12

1: No matter what, immediately get one side to equal 0 2: If possible, factor x²+5x+6=0 (x+3)(x+2)=0 **x=-3 or x=-2** 2: If factoring's too hard, Quadratic formula _-5±√(5)²-(4✖1✖6)_ 2(1) _-5±√1_ 2 _-5+√1_ = **-2=x** or _-5-√1_ = **-3=x** 2 2 3. If all else fails, complete the square x² – 4x – 8 = 0 x² – 4x=8 x² – 4x + 4= 8+4=12 (x-2)²=12 x-2= _+_√12 x=2+√12 or x=2-√12 **x=2+2√3 x=2-2√3**

Answer 13

DON'T divide by X DON'T forget ± when √

Answer 14

Cone: 1/3πr²h Pyramid: 1/3(area of base)h Sphere:4/3πr³

Answer 15

Circumference: πd Area: πr²

Answer 16

A=P(1+(r/n))^nt r=decimal of %rate (eg 10%=.10) t=number of years n=times compounded per year Continuous: A=Pe^rt e=Mathematical constant r=decimal rate t=number of years

Answer 17

P(.5)^{t/half life}=amount Example: 6.6g initial 14 day half life How long til 1 gram? 6.6(.5)^t/14=1 ln(6.6) + ln(.5)(t/14)=ln(1) ln(6.6) + ln(.5)(t/14)=0 ln(.5)(t/14)=-ln(6.6) t/14=(-ln(6.6))/(ln(.5)) x 14 **t=38.11 days!**

Answer 18

The point where the concavity of a graph changes

Answer 19

[.......] = inclusive (......) = not inclusive The domain of the logistic function is all real numbers, which could be stated either with words or by writing (-∞, +∞) nb Infinity is always not inclusive The range of the logistic function is between y=0 and y=1, not inclusive, which would be written (0, 1)

12 Basic Functions Flashcards

(44 cards)