Questions and Answers

8/18/07
QUESTION:  On 39 are we able to graphically find the domain and range of the function or do we have to find them through algebraic methods? And also I still don't know what to do like on 39c) with the whole "x<0 and >or equal to 0" part. I don't no if I graph vertical lines or if it restricts the function. I just don't remember what it does.

ANSWER:  On #39, You should be able to determine the domains algebraically, but the ranges are allowed to be determined by their graphs.   For t 39C, the inequalities are restrictions on the domains for each piece of the function.  There shouldn't be any vertical lines.

QUESTION:  For number 19 I'm very confused here. Are you allowed to have more than two intercepts but must have intercepts at x=-2 and x=2. I was thinking about it and the only way you can have exactly and have only two intercepts was if you had a parabola, but when you have a parabola it doesn't have odd (origin) symmetry. And since you can determine how many intercepts an equation has you can look at the highest power of the equation and you can figure it out. So are we allowed to have an equation with more than two intercepts but pass through the two points?

ANSWER:  Your reasoning above is very sound and it is correct when applied to POLYNOMIAL functions.  However, you are being too limited in your thinking...consider rational functions that might also have asymptotes (vertical, horizontal, or slant) or graphs that make tilted hyperbolas (like y=1/x for example). 

 

8/3/07
QUESTION:  For number39, when you graph Y= the square root of X does it graph onto both sides of the graph or just one. When doing it on the graphing calculator it only graphs on one, but for some reason i remember you saying that it goes on both. Is that right?

ANSWER:  The graph of y=sqrt(x) is only graphed above the x-axis.  There is no graph beneath it unless there is a plus/minus sign in front of the radical (which is not present for this problem).

QUESTION:  For numbers 37 and 38. I am not sure what evaluate means. Does it mean just substitute the number(s) with F into the problem and solve for X or what?

ANSWER:  Evaluate means you plug the number given in the parentheses into the formula for x and compute the answer.  There is no "solving for x" because you substituted the number in for it and there aren't any x's in the expression.  You just simplify it to a single numerical answer (if possible).

QUESTION:  On number 42B I think I have the whole equation worked out correctly except I cannot get the graph to shift two to the right. I tried using transformation stuff but because nothing is being multiplied I don't think it will work.

ANSWER:  You're on the right track with the transformation stuff.  Where do you place constants into a function to designate a horizontal shift?  Hint: Remember to use the opposite sign with horizontal translations, and remember that parentheses are necessary.

QUESTION:  On numbers 43 and 48-50 I am just not sure how to write the problems out as a function of X. For some reason I cant figure this out! Just a boost in the right direction PLEASE!

ANSWER:  To write area as a function of x means, A(x)=some expression containing only x-variables.  When you start out with these types of problems, you often have a picture with x's and y's labeled for the dimensions.  Area=length*width might be written as A=xy, but then you have to substitute another expression for the y so that only x's are in the final equation.

QUESTION:  Lastly numbers 44 and 45, I don't remember how to find an equation for the tangent line to the circle at a certain point. Again I just need a little push in the right direction

ANSWER:  To write an equation for any line, what two pieces of information do you need?  A point and a slope.  So to write an equation for a specific tangent line, the point will be the one point of intersection on the circle, and you will need to determine the slope of it.  Hint:  Remember that a radius drawn to any point of tangency is always perpendicular to the tangent line, so you will have to work with perpendicular slopes to figure this out.