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Section 1.2 #56: Find the domain of the function f(x)=8x+4.
Solution: The domain of this function can be found by considering where the denominator equals zero. So we require the denominator to be nonzero, i.e. x+40. Isolating x shows us that x4. Therefore the domain of f is R{4} (or written as (,4)(4,) or written as {x:xisarealnumberandx4} or written as "all real numbers except x=4" or written as "<x<4 or 4<x<").

Section 1.2 #66: Find the domain and range of the function whose graph is pictured:

Solution: The domain is the set of inputs which have an output. That means we are looking for where on the x-axis has a point shaded in above or below it, i.e. the interval [2π,2π]. You may also write this domain in the following ways: 2πx2π or "all real numbers between 2π and 2π, including both 2π and 2π".

The range is the set of numbers which are actually outputted by the function. To find it, look up and down the y-axis for the places which have a shaded dot to the left or right of the y-axis -- i.e. [1,1].

Section 1.3 #6: Find the slope of the line containing the points (3,1) and (3,5).
Solution: Recall the slope of the line containing the points (x1,y1) and (x2,y2) is slope=m=y2y1x2x1. Therefore we compute slope=m=513(3)=66=1. Section 1.3 #32: Find the slope of the graph of the linear equation y=25x+7.
Solution: This equation is already in slope-intercept form. Therefore we may "read off" the slope as the coefficient of x, i.e. the slope is 25.

Section 1.3 #55: Find the slope and the y-intercept of the line with equation 3x+2y=10.
Solution: This equation is not in "slope-intercept" form, so it is not as straightforward as #32 to answer the question. One way to proceed is to algebraically manipulate the equation into slope-intercept form: start with 3x+2y=10,

subtract 3x from both sides to get 2y=3x+10, divide both sides by 2 to get y=32x+5. This equation is equivalent to the original and is in slope-intercept form. Therefore we see the slope is 32 and the y-intercept is (0,5). (note: if you ask WolframAlpha to find the y-intercept, it only reports "5" -- their definition of y-intercept is not as a point like ours is...be careful!)