I need help with these two questions please.

9514 1404 393

Step-by-step explanation:

1. The denominator in the first part of the function definition factors as ...

  x² +x -2 = (x -1)(x +2)

This has zeros at x = -2 and x = 1, which will be values of x excluded from the domain. (These zeros are in the domain x < 2, which is applicable to this part of the function definition.)

The second part of the function definition is defined for all x ≥ 2, so the only exclusions are x = -2 and x = 1. The domain of the piecewise function is ...

  (-∞, -2)∪(-2, 1)∪(1, ∞)

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2. It is helpful to take a look at the graph to see what the axis labels are. The x-axis is labeled "number of cupcakes", so "12" on that axis means "12 cupcakes". The y-axis is labeled "total cost", which we are to presume is in dollars. That means the slope of the graph is Δy/Δx = "dollars per cupcake", the cost of one cupcake.

We observe that the slope of the graph decreases at x=12. This means the cost of a cupcake goes down after 12 are purchased. The appropriate description is ...

  The first 12 cupcakes cost $2 each, and all cupcakes after that cost $1 each.

(The other choices have either increasing slope at the breakpoint, or a different breakpoint, or both, so cannot be right.)

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.