Can you help me on how to identify Linear, Quadratic,and etc. functions from tables, graphs, and equation?

Question

linear, quadratic, exponential, absolute value, and square root

Answer 1

linear: graph is a straight line that is not vertical. table shows values steadily increasing or decreasing.

quadratic: graph looks like a "U" - either up (v) or down (^) and either wide opening or small opening. table shows values decreasing/increasing rapidly, then slowly, then the opposite direction, such as:
x: 1 2 3 4 5 6 7 8 9
y: 16 8 4 2 1 2 4 8 16

exponential: similar to the quadratic, but it increases more rapidly, has y=1 when x=0, and does not "go the opposite direction" like the quadratic does. it starts out very little, like a fraction, then shoots up and doesn't come back. the table is like that: starts out little, increases a little, increases more and more rapidly, then its too big.

absolute value: looks like a "V", not like a quadratic that looks like a "U". absolute values have an indifferentiable point, or in other words the bottom tip of the "V". it's like a linear equation that is positive on one side where it should be negative. the table is like a linear, but always positive where it should be negative.

square root: looks like half a "U" turned 90 degrees clockwise on its side and only positive. starts along the x-axis with y=0 at some x, then increases rapidly for a short time, then increases very slowly afterwards.
x: 1 2 3 4 5 6 7 8
y: 0 .5 .9 1.2 1.4 1.5 1.55 1.57

note that the sample tables are not representing real functions, they just graph a general idea of what it should look like.

Answer 2

a linear graph, as the name suggests, is a straight line. Its equation is a constant times x plus another constant. A quadratic equation has an x^2 term in it, and it's a curve. A quartic or x^any even number looks a bit like a quadratic; a bowl-shaped curve, either the right way up or upside down. X to the power of an odd number gives you a curve that
goes up or down with a few kinks usually. Exponential curves get steeper and steeper very quickly, or flatter and flatter very quickly. A square root curve climbs steeply at first, then gets less steep, like your average gentle well-weathered hill. Absolute value graphs all show a discontinuity at x=0. The negative side is a mirror image of the positive side. The quickest way to learn all this, and remember it, is to invest about US$60 in a graphing calculator and play around with it.

Answer 3

Linear
ax + by = c and y = ax + b are both linear problems, The graph of them looks like a diagonal line.

Quadratic
y = ax^2 + bx + c looks like a right-side up or up-side down U.

Cubic
y = ax^3 + b looks like half a U on the right side, and the inverse of that half on the left side

Exponential
y = ex^a or y = log(x) starts at the bottom and travels upward or starts at the top and travels downward.

Absolute Value
y = a|x| + b, looks like a V shape

Square Root
y = asqrt(x) looks like a U that goes to the left or right. Its like the quadratic graph, only instead of up or down, its left or right. Also don't forget that a sqrt graph has both a negative and positive.

Answer 4

a. graph of linear equation showing a straight linear line
b. graph of quadratic equation showing two peaks
c. graph of exponential equation showing a typical accelated curve
d. graph of a 3rd order equation showing three peaks
e. graph of absoloute equation showing mirroring of negative axis and positive axis

Answer 5

u jss do u stupid