Someone please help. Ill give you brainiest.
1 answer:
19. The absolute value equation of the graph is: y — | x - 0 | + 2 where (0,2) is the vertex.
Domain: (-∞, ∞)
Range: (-∞, 2]
A function is a relation in which no two ordered pairs have the same first component (inputs/x-values/domain) and different second components (outputs/y-values/range).
In determining whether a given relation is a function, we need to ask ourselves, does every first element (or input) correspond with EXACTLY ONE second element (or output)?
In the case of an absolute value function, its relation is a function because each input corresponds to exactly one output. To demonstrate, I performed a Vertical Line test to show why it is a function.
The Vertical Line Test (VLT) allows us to know whether or not a graph is actually a function. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function. As the attached graph of the absolute value function, EACH vertical line drawn crosses the graph only once. This graph passes the VLT, making it a function.
20.)
The set of first components (x-coordinates) in the ordered pairs is the DOMAIN of the relation.
The set of second components (y-coordinates) is the RANGE of the relation.
Domain: {-2, -1, 0, 1}.
Range: {4, 3, 2, 1, 0}.
The given relation is NOT a function. As you can see from the given diagram, the input value of 2 corresponds to two output values: 4 and 0.
Please mark my answers as the Brainliest if you find my explanation helpful :)
Domain: (-∞, ∞)
Range: (-∞, 2]
A function is a relation in which no two ordered pairs have the same first component (inputs/x-values/domain) and different second components (outputs/y-values/range).
In determining whether a given relation is a function, we need to ask ourselves, does every first element (or input) correspond with EXACTLY ONE second element (or output)?
In the case of an absolute value function, its relation is a function because each input corresponds to exactly one output. To demonstrate, I performed a Vertical Line test to show why it is a function.
The Vertical Line Test (VLT) allows us to know whether or not a graph is actually a function. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function. As the attached graph of the absolute value function, EACH vertical line drawn crosses the graph only once. This graph passes the VLT, making it a function.
20.)
The set of first components (x-coordinates) in the ordered pairs is the DOMAIN of the relation.
The set of second components (y-coordinates) is the RANGE of the relation.
Domain: {-2, -1, 0, 1}.
Range: {4, 3, 2, 1, 0}.
The given relation is NOT a function. As you can see from the given diagram, the input value of 2 corresponds to two output values: 4 and 0.
Please mark my answers as the Brainliest if you find my explanation helpful :)
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Answer:
Isolate the variable by dividing each side by factors that don't contain the variable
Exact Form:
x = - 25/8
Decimal Form:
x = -3.125
Mixed Number Form:
x = - 3/1/8
Step-by-step explanation:
well, about A and D, I just plugged the values on the slope formula of
for A the values are 8.01 and 8.0, so indeed those "slopes" are close.
for D the values are -2.25 and 8.0, so no dice on that one.
for B, let's check the y-intercept for g(x), by setting x = 0, we end up g(0) = 0³-4(0)+1, which gives us g(0) = 1.
checking L(x) y-intercept, well, L(x) is in slope-intercept form, thus the +1 sticking out on the far right is the y-intercept, so, dice.
for C, well, the slope if L(x) is 8, since it's in slope-intercept form, the derivative of g(x) is g'(x) = 3x² - 4, and thus g'(0) = -4, so no dice.
for E, do they intercept at (2,1)? well, come on now, L(x) is a tangent line to g(x), so that's a must for a tangent.
for F, we know the slope of the line L(x) is 8, is g'(2) = 8? let's check
recall that g'(x) = 3x² - 4, so g'(2) = 3(2)² - 4, meaning g'(2) = 8, so, dice.