Given the equation y=2x-4 of an exponential function f
1)write down the equation of horizontal asymptote of f
2)determine the y intercept of f
3)determine the y value of a point on f with x=-2
4)draw the graph of the function of f showing all critical poins and asymptotes
5)determine the domain and range
y = 2x - 4 is not an exponential function, it is linear and its graph is a straight line
To answer the given questions about the exponential function f with the equation y=2x-4, let's go step by step:
1) The equation y=2x-4 is not an exponential function. It is a linear function since the exponent of x is 1. Therefore, it does not have a horizontal asymptote.
2) To find the y-intercept of the linear function, we set x=0 and solve for y:
y = 2(0) - 4
y = -4
So, the y-intercept of the function f is -4.
3) To determine the y-value of a point on f when x=-2, we substitute x=-2 into the equation:
y = 2(-2) - 4
y = -4 - 4
y = -8
So, the y-value of the point on f with x=-2 is -8.
4) Since the given equation y=2x-4 is a linear function, the graph will be a straight line. You can plot the graph by selecting a few x-values, calculating the corresponding y-values using the equation, and then connecting the points. Since there are no critical points or asymptotes in a linear function, there is no need to indicate them on the graph.
5) The domain of the function f is the set of all possible x-values that the function can take. Since it is a linear function, the domain is all real numbers (-∞, ∞). The range of the function is the set of all possible y-values that the function can produce. Again, since it is a linear function, the range is also all real numbers (-∞, ∞).
1) The equation y=2x-4 represents a linear function, not an exponential function. Linear functions do not have a horizontal asymptote. However, if you meant to write the equation of a horizontal line, then the equation of the horizontal asymptote is y = -4.
2) To find the y-intercept of the linear function y=2x-4, we set x=0 and solve for y. Thus, y = 2*0 - 4 = -4. Therefore, the y-intercept of the function is -4.
3) To determine the y value of a point on the function f when x = -2, we substitute x = -2 into the equation and solve for y. Thus, y = 2*(-2) - 4 = -8. Therefore, the y value of the point on the function f with x = -2 is -8.
4) Since the equation y=2x-4 represents a linear function, the graph will be a straight line. To draw the graph, plot two points on the line, such as (0, -4) and (1, -2), and then draw a straight line through these points. There are no critical points or asymptotes for this linear function since it is a straight line.
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-8 | .
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-6 |
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-4 | *
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-2 |
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0 | _______________
| x
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5) The domain of the linear function y=2x-4 is all real numbers since there are no restrictions on the input variable x. Therefore, the domain is (-∞, ∞). The range of the function is also all real numbers since the function can take on any y value. Therefore, the range is (-∞, ∞).