Given the graphs for functions f(x) and g(x).Find the following:
Please help asap.
Answers
Answer:
- f(x): vertical, x = -4; horizontal, y = 3
- g(x): vertical, x = 2; horizontal, y = -4
- g(x) is shifted right 6 and down 7 from f(x)
Step-by-step explanation:
The vertical asymptote is the vertical dashed line in each graph. Its equation is x = constant, where the constant can be read from the graph where the line crosses the x-axis.
The horizontal asymptote is the horizontal dashed line in each graph. Its equation is y = constant, where the constant can be read from the graph where the line crosses the y-axis.
f(x)
The vertical asymptote is x = -4. The horizontal asymptote is y = 3.
g(x)
The vertical asymptote is x = 2. The horizontal asymptote is y = -4.
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The vertical asymptote of g(x) is 2-(-4) = 6 units to the right of that of f(x). The horizontal asymptote of g(x) is -4-3 = -7 units up from that of f(x). The graph of g(x) matches that of f(x) shifted right 6 units and down 7 units.
To find the intersection points of two graphs, set f(x) equals to g(x) and solve for 'x'. Substituting the x-value into either function gives the y-coordinate. The intersection point is the (x, y) pair.
In the subject of Mathematics, to find the specific points where function f(x) and function g(x) intersect, we need to set them equal to each other and solve for the variable x.
The formula we use is f(x) = g(x).
If f(x) is a linear equation such as y = 2x + 3 and g(x) is also a linear equation such as y = -3x + 7, setting them equal gives 2x + 3 = -3x + 7.
Solving for x ends up with x = 0.8. This x value is where the two functions intersect on a graph.
Another step can be taken to find the y coordinate by substituting the x value into either function.
So, if we substitute 0.8 into the function f(x), f(0.8) = 2(0.8) + 3 = 4.6. So the intersection point is (0.8, 4.6).
Learn more about Intersection of functions here:
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Answers
Answer:
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Step-by-step explanation:
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