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Algebra, Trig
Algebra-Trig
Find the slope of the line that goes through the following points: (-4, 6), (-8, 6)
Slope: m = (y2 -- y1) / (x2 -- x1) = (6 -- 6) / (-8 -- (-4)) = 0 / (-4) = 0
m = 0.
Determine whether the given function is even, odd or neither: f (x) = 5x^2 + x^
To test a function for even, odd, or neither property, plug in -- x for x, and simplify.
f (-x) = 5(-x)^2 + (-x)^4 = 5x^2 + x^4.
Because the final expression remains the same for -- x, it stands that the function is even.
f (x) is even.
Find the slope of the line that goes through the following points: (-1, 1), (-2, -5)
Slope: m = (y2 -- y1) / (x2 -- x1) = ((-5) -- 1) / ((-2) -- (-1)) = (-6) / (-1) = 6
Answer: m = 6.
Evaluate: f (x) = -5x + 8 at f (-3)
f (-3) = -5(-3) + 8 = 15 + 8 = 23
Answer: f (-3) = 23.
Evaluate: f (x) = 3x^2 -- 4x -- 3 at f (x -- 1)
f (x -- 1) = 3(x -- 1)^2 -- 4(x -- 1) -- 3 = 3(x^2 -- 2x + 1) -- 4x -- 4 -- 3
= 3x^2 -- 6x + 3 -- 4x -- 7 = 3x^2 -- 10x -- 4
Answer: f (x -- 1) = 3x^2 -- 10x -- 4.
6. Determine whether the given function is even, odd, or neither: f (x) = x^3 -- 5x
To test a function for even, odd, or neither property, plug in -- x for x, and simplify.
f (-x) = (-x)^3 -- 5(-x) = -x^3 + 5x
Because the final expression is the exact opposite of f (x), it stands that the function is odd
Answer: f (x) is odd.
7. Find the domain and range of: {(7, -2), (-6,-4), (-9,-9),(-5,-5),(6,6)}
Domain is all values of x: 7, -6, -9, -5, 6
Range is all values of y: -2, -4, -9, -5, 6
Answer: Domain = {-9, -6, -5, 6, 7}, Range = {-9, -5, -4, -2, 6}.
8. The following relation is a function: {(-3,-4),(3,3),(5,-6),(8,1),(11,-5)}. True or false
A working definition of a function defines that for any x, there is exactly one yield of y. In this case, the relation of numbers given yield exactly one y. Therefore, the relation is a function.
Answer: True.
9. Determine the slope m and the y-intercept for y + 9 = 0
Slope-intercept formula: y = mx + b y = -9, therefore slope m = 0
Answer: m = 0, y = -9.
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