1.f(x)=x^2

2.f(x)=x^2-6

3.f(x)=x

4.f(x)=x+3

state the domains, range and intercept : y=2^x

(how do u find the domain and range with and without a Ti-84 Plus?)

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1.f(x)=x^2

2.f(x)=x^2-6

3.f(x)=x

4.f(x)=x+3

state the domains, range and intercept : y=2^x

(how do u find the domain and range with and without a Ti-84 Plus?)

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## Answers (2)

Graphically: odd functions become "upside down" after crossing the y axis and are the same if you flip them around the origin 180˚. Even functions are symmetric through the y-axis, so the left is the mirror image of the right

Algebraically: see if f(-x) = -f(x) or f(x)

1: f(-x) = (-x)^2 = x^2 = f(x) ==> even function

2: f(-x) = (-x)^2 - 6 = x^2 - 6 = f(x) ==> even

3: f(-x) = -x = -f(x) ==> odd

4: f(-x) = -x + 3 ==> neither

Shortcut:

Any even power of x is an even function (that includes x^0). Any odd power of x is an odd function. If you add two even functions, you get another even function. If you add two odd functions, you get an odd function. If you add two different kinds of functions, then the result is neither odd nor even.

y=2^x:

With the calculator:

See the general shape of the graph: there is an asymptote at y = 0, and the function continues upward on the right side. Since there are no discontinuities, the domain is all real numbers. The range is x>0, or

(0,∞)

Without:

First question: are there any discontinuities?

answer: no, 2 can be taken to any power and yield a real number

Second question: are there any absolute maxima or minima?

answer: no

Third question: if not, what happens when you make x really big? really small?

Answer: 2 to a very high power is a very high number, so x-> ∞. To to a very small number is 1/(a very high number) which is close to 0. So, x->0. So your range is (0,∞)

intercept: y(0) = 2^(0) = 1, the y intercept is 1. There is no x-intercept

even functions are functions are symmetric about the y-axis.

odd functions symmetric about the X.

Domain is just the x values

and range is y values.

intercept just look where x or y = 0.