Algebra graph each function...?
step 1: plot points (1,1), (1/2, 2), (2, 1/2), (-1,1), (-2,-1/2), (-1/2, 2), etc. sketch the curve. domain: x does not equal 0 range: Some would say that real numbers is sufficiently precise, but y not equal to 0 would be more precise. compare to the graph of y = -10 /x multiplying by a negative number reflects the graph across the x axis. and 10 applies a stretch factor.
College algebra: graph functions to answer domain,range, explanation?
Graphically, a domain is how far across the x-axis a graph spans. A range is how far up and down the y-axis a graph stretches. Some graphs, like y = x^2, are limited in range. In this case, y can never be less than 0, so the range is y>=0. x in this case can be anything, so the domain for x is all real numbers. Graphically that makes sense - you can graph your parabola as far left and right that you want to, but not up and down. Other graphs, like y = sin x, are even more limited in the y direction. Graphically, you can see that y can't go past -1 or 1, so the range is -1 <= y <= 1. And still others have no bounds. y = x exists everywhere - there's no limit on what x or y can be. This is probably a lead-in to graphing more advanced functions, such as y = (x^2 - 1)/(x + 1), where you'll have a domain of all real values except for x = -1. As you can tell, the function can't exist at x = -1 because you'll have a 0 denominator. So graphically, you'll have problems with that. (You'll end up drawing an open circle at that point to indicate that it doesn't exist there.)
College Algebra Functions Question?
f(x) =√(x³-64x) f(x) is real only if √(x³-64x) is real which requires that (x³-64x) not be negative. Now, the question is when is (x³-64x) not negative? Consider the graph of the cubic function y = x³-64x = x(x+8)(x-8): i. Since the coefficient of x³ is positive, the graph of y=x³-64x goes from lower left to upper right. ii. It's zeros are x= -8, 0, 8 iii. So, its graph goes up from the lower left to cross the x-axis at -8. Then, it turns down to cross the x-axis at 0. Then it turns upward to cross the x-axis at 8 and continues on upward and to the right. iv. So, y=x³-64x is not negative on the intervals [-8,0] & [8,inf) ... i.e. where the graph is not below the x-axis. ANSWER It follows that the domain of f(x) =√(x³-64x) is [-8,0]U[8,inf) so that the least value in the domain of f(x) is x= -8 http://www.quickmath.com/webMathematica3... Have a good one!
College algebra?
Consider the following. − (-4/3, −9) (a) Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. (x, y) = (b) Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. (x, y) =
Graphing College Algebra question on Asymptotes?
Let's first find the vertical asymptotes. These occur where the denominator is 0. x² - 9 = 0 x² = 9 x = (+/-) 3 The horizontal asymptote is the constant on the end of the hyperbola, in this case we don't have a constant so the horizontal asymptote is y = 0. The slant asymptote is the numerator of the remainder, if it is a function, when dividing these. Let's use long division. ·········______ x² - 9 | x² - 1 x² - 9 goes into x² -1, one time and gives a new divisor of 8 x² - 9 goes into 8, (8 / x²-9) times Ans: 1 + ((8) / (x² - 9)) Since the numerator is a constant there is no slant asymptote To find the y intercept plug in 0 for x 0 - 1 / 0 - 9 -1/-9 1/9 Answer: Vertical Asymptotes, x = -3, 3 Answer: Horizontal Asymptote, y = 0 Answer: Slant asymptote, None Answer: Y intercept, y = 1/9 I hope this helps. Have a good day.
College algebra help?!?
from a 15 inch by 15 inch piece of metal, squares are cut out of the four corners so that the sides can then be folded up up to make a box. Let x represent the lenth of sides of the squares in inches that are cut out. express the volume of the box as a function of x, graph the function and from the graph determind the value of x, to the nearest tenth of an inch, that will yield the maximum value
College Algebra, So confused on these 5 questions?
1.) Make a table of the values of each function and plot the points to graph the function by hand. F(x)=3x^2 ------that's the problem, the thing is I know how to graph it, but unsure how I get the table and what numbers go into the table. 2.) Suppose F(x)=100x^2-5x thousands units are produced , where x is the number of years after 2000. A. What is f(10) B. How many units are produced in 2010, according to this function? 3.)Find the x-intercepts of the graph of the given equation, if they exist, and b graph the equation. x+5y=17 -------------------- I did the work, but was told it was wrong and to fix it. Well how can I fix it I gave it my best shot the first time! 4.)Write the equation of a line with the given function Slope -1/2 and y intercept is -8 5.) For the functions , use F(x+h)-f(x)/h f(x)=32x+12 f(x)=3x^2+1 I did a bunch of problems already and tried to fix them myself. My book doesnt give examples and my professor well she just doesnt care if you understand it or not. Can somebody help me with the 5 I'm unsure about and explain and show work of how you came to an answer PRETTY PLEASE!!