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Given that (7-6) is on the graph f(x) find the corresponding point for the function f(x plus 2)?
When the x coordinate is changed by adding a constant amount this is the same as translating (shifting) the graph of the function f(x) that amount parallel to the x-axis; if the amount is positive the graph is translated to the left, if it is negative it is translated to the right.
As (7, -6) is on f(x), then under the translation f(x + 2), the graph is translated to the left (2 x-values), so the point (7-2, -6) which is the point (5, -6) is the corresponding point on the graph to (7, -6).
What else can I help you with?
If (4 -5) is on the graph of F(x) which point must be on the graph of the inverse function F -1(x)?
If the point (4, -5) is on the graph of the function F(x), then the point (-5, 4) must be on the graph of the inverse function F⁻¹(x). This is because the inverse function swaps the x and y coordinates of the original function's points. Therefore, for every point (a, b) on F(x), the corresponding point (b, a) will be on F⁻¹(x).
How does the graph of an exponential function differ from the graph of a linear function and how is the rate of change different?
The graph of a linear function is a line with a constant slope. The graph of an exponential function is a curve with a non-constant slope. The slope of a given curve at a specified point is the derivative evaluated at that point.
How is the initial value of a function represented in a a table and in a graph?
In a table, the initial value of a function is typically represented as the output corresponding to the input value of zero, often found in the first row of the table. In a graph, the initial value is shown as the y-coordinate of the point where the graph intersects the y-axis, which corresponds to the function's value when the input (x) is zero. This point serves as a starting point for understanding the behavior of the function.
Explain How do you use a graph to find the output value of a linear function for a given input value?
To find the output value of a linear function for a given input value using a graph, first locate the input value on the x-axis. Then, trace a vertical line upwards from that point until it intersects the line representing the linear function. Finally, from the intersection point, move horizontally to the y-axis to read the corresponding output value. This process visually demonstrates the relationship between the input and output in the function.
How do you get the tangent line without the graph?
The answer will depend on the context. If the curve in question is a differentiable function then the gradient of the tangent is given by the derivative of the function. The gradient of the tangent at a given point can be evaluated by substituting the coordinate of the point and the equation of the tangent, though that point, is then given by the point-slope equation.
Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even?
If the point (x,y) is on the graph of the even function y = f(x) then so is (-x,y)
If (4 -5) is on the graph of F(x) which point must be on the graph of the inverse function F -1(x)?
If the point (4, -5) is on the graph of the function F(x), then the point (-5, 4) must be on the graph of the inverse function F⁻¹(x). This is because the inverse function swaps the x and y coordinates of the original function's points. Therefore, for every point (a, b) on F(x), the corresponding point (b, a) will be on F⁻¹(x).
How does the graph of an exponential function differ from the graph of a linear function and how is the rate of change different?
The graph of a linear function is a line with a constant slope. The graph of an exponential function is a curve with a non-constant slope. The slope of a given curve at a specified point is the derivative evaluated at that point.
How do you determine if the graph is a function?
If for every point on the horizontal axis, the graph has one and only one point corresponding to the vertical axis; then it represents a function. Functions can not have discontinuities along the horizontal axis. Functions must return unambiguous deterministic results.
How do you figure out the starting point of a distance vs time graph when given the velocity vs time graph and a function?
To find the starting point of a distance vs time graph from a velocity vs time graph and a function, you would integrate the velocity function to find the displacement function. The starting point of the distance vs time graph corresponds to the initial displacement obtained from the displaced function.
How is the function differentiable in graph?
If the graph of the function is a continuous line then the function is differentiable. Also if the graph suddenly make a deviation at any point then the function is not differentiable at that point . The slope of a tangent at any point of the graph gives the derivative of the function at that point.
What are the uses of derivatives?
A derivative of a function represents that equation's slope at any given point on its graph.
What are uses of derivatives?
A derivative of a function represents that equation's slope at any given point on its graph.
What is the zero of a function and how does it relate to the functions graph?
A zero of a function is a point at which the value of the function is zero. If you graph the function, it is a point at which the graph touches the x-axis.
How is the initial value of a function represented in a a table and in a graph?
In a table, the initial value of a function is typically represented as the output corresponding to the input value of zero, often found in the first row of the table. In a graph, the initial value is shown as the y-coordinate of the point where the graph intersects the y-axis, which corresponds to the function's value when the input (x) is zero. This point serves as a starting point for understanding the behavior of the function.
Explain How do you use a graph to find the output value of a linear function for a given input value?
To find the output value of a linear function for a given input value using a graph, first locate the input value on the x-axis. Then, trace a vertical line upwards from that point until it intersects the line representing the linear function. Finally, from the intersection point, move horizontally to the y-axis to read the corresponding output value. This process visually demonstrates the relationship between the input and output in the function.
How do you get the tangent line without the graph?
The answer will depend on the context. If the curve in question is a differentiable function then the gradient of the tangent is given by the derivative of the function. The gradient of the tangent at a given point can be evaluated by substituting the coordinate of the point and the equation of the tangent, though that point, is then given by the point-slope equation.
