Question 764576: Can someone please help me with this. It is due tonight before midnight and I am so confused.
Graph the function, state the domain and range: f(x)=4
Graph the relation, state the domain and range: x=(y+2)^2.
Mention any key points on the graphs, including intercepts, vertex, or start/end points. Discuss the general shape and location of each of your graphs. State the domain and range for each equation, write them in interval notation. State whether each of the equations is a function. Select one of the graphs and assume it has been shifted 3 units upward and 4 units to the left. Discuss how the transformation effects the equation by rewriting the equation to incorporate those numbers.
This is making me stressed by the minute. Can someone please help me with this. I would surely appreciate it.
Found 2 solutions by stanbon, rothauserc:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Graph the function, state the domain and range: f(x)=4
Plot two points and draw a line thru them:
(0,4); (3,4)
Domain::: All Real Numbers:: (-oo,+oo)
Range:::[4]
y-intercept:: (0,4)
x-intercepts:: none
It is a functon.
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Graph the relation, state the domain and range:
x=(y+2)^2.
Not a function.
Parabola opening to the right from vertex (0,-2)
Domain: All Real Numbers >= -2; [-2,+oo)
Range: All Real Numbers:: (-oo,+oo)
Note: Relations cannot be graphed on this site.
y-intercept:: (0,-2)
x-intercept: (4,0)
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Shirting 3 up and 4 to the left gives
x+4 = (y+2)^2 + 3
Modify to: x = (y+2)^2-1
Mention any key points on the graphs, including intercepts, vertex, or start/end points. Discuss the general shape and location of each of your graphs. State the domain and range for each equation, write them in interval notation. State whether each of the equations is a function. Select one of the graphs and assume it has been shifted 3 units upward and 4 units to the left. Discuss how the transformation effects the equation by rewriting the equation to incorporate those numbers.
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Cheers,
Stan H.
Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! f(x) = 4, means y = 4, this is a horizontal line at (0,4) and parallel to the x axis.
x = (y+2)^2
y+2 = sqrt(x) and
y = sqrt(x) - 2
let's look at the graphs of both functions
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f(x) = 4 is the red horizontal line 4 units above the x axis
its domain is -infinity to +infinity and its range is 4
this is a function with no x intercept but y intercept is (0,4)
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y = sqrt(x) - 2 is the green line in the first and second quadrants
its domain is x greater than or equal to 0 and range is -2 to +infinity
This is a function with x intercept (4, 0) and y intercept is (0, -2)
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select y = sqrt(x) - 2
assume it has been shifted 3 units upward and 4 units to the left
an upward shift is defined as g(x) = f(x) + c, where c is 3 in this case
a shift to the left is defined as g(x) = f(x+c), where c is 4 in this case
putting both shifts together we have
y = sqrt(x+4) + 1
let's look at this graph
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