Yes it does
The same as multiplying any other function by a negative number - after multiplying, positive numbers will become negative numbers, and vice versa.
Multiplying a function by -1 will make it a reflection of the original function across the x axis.
Multiplying a function by negative one reflects its graph across the x-axis. This means that all the y-values of the function are inverted, turning positive values into negative ones and vice versa. Consequently, any point (x, y) on the original graph will be transformed to (x, -y) on the new graph. This reflection alters the orientation of the graph without changing its shape or the x-values.
When a function is multiplied by a number between 0 and 1, the graph of the function is vertically compressed. This means that all the y-values of the function are scaled down, resulting in a graph that appears shorter while maintaining its original shape. The x-intercepts remain unchanged, but the maximum and minimum values of the graph decrease, making the function approach the x-axis more closely without crossing it.
Yes it does
x
When a function is multiplied by -1 its graph is reflected in the x-axis.
The same as multiplying any other function by a negative number - after multiplying, positive numbers will become negative numbers, and vice versa.
Multiply by -1
Multiplying a function by -1 will make it a reflection of the original function across the x axis.
Multiplying a function by negative one reflects its graph across the x-axis. This means that all the y-values of the function are inverted, turning positive values into negative ones and vice versa. Consequently, any point (x, y) on the original graph will be transformed to (x, -y) on the new graph. This reflection alters the orientation of the graph without changing its shape or the x-values.
When a function is multiplied by a number greater than 1, the graph of the function is vertically stretched. This means that all the y-values of the function are increased, making the graph rise more steeply compared to the original. Consequently, points on the graph move away from the x-axis, resulting in a steeper appearance without changing the x-intercepts.
When a function is multiplied by a number between 0 and 1, the graph of the function is vertically compressed. This means that all the y-values of the function are scaled down, resulting in a graph that appears shorter while maintaining its original shape. The x-intercepts remain unchanged, but the maximum and minimum values of the graph decrease, making the function approach the x-axis more closely without crossing it.
The relationship between a logarithmic function and its graph is that the graph of a logarithmic function is the inverse of an exponential function. This means that the logarithmic function "undoes" the exponential function, and the graph of the logarithmic function reflects this inverse relationship.
No, a circle graph is never a function.
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