They mean the graph/function is decreasing.
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).
The straight line in the graph goes 'uphill' from left to right
If the graph is not a straight line, then it has different slopes at different points, and there's no easy general way to measure it. It's a lot easier if the graph is a straight line. Here's how to do it: -- Mark off a section of the line, and ignore the rest of it. -- Measure how much that part of the line rises from its left end to its right end. That's the change in 'y'. -- Measure how much of the 'x' axis that part of the line covers, from its left end to its right end. That's the change in 'x'. -- Divide (the change in 'y') by (the change in 'x'). The result of the division is the slope of the line.
The linear parent function is y=x. The line on a graph passes through the origin(0,0) with a slope of 1. The line will face left to right on the graph like this /.
It is a function whose graph starts in the top left and goes to the bottom right. There could be some intervals in which the graph moves upwards to the right. This follows from the definition of average rate of change.
Right-click on the graph and select Change Chart Type.
They mean the graph/function is decreasing.
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).
The straight line in the graph goes 'uphill' from left to right
If the graph is not a straight line, then it has different slopes at different points, and there's no easy general way to measure it. It's a lot easier if the graph is a straight line. Here's how to do it: -- Mark off a section of the line, and ignore the rest of it. -- Measure how much that part of the line rises from its left end to its right end. That's the change in 'y'. -- Measure how much of the 'x' axis that part of the line covers, from its left end to its right end. That's the change in 'x'. -- Divide (the change in 'y') by (the change in 'x'). The result of the division is the slope of the line.
The linear parent function is y=x. The line on a graph passes through the origin(0,0) with a slope of 1. The line will face left to right on the graph like this /.
base
the left end of the graph is going in a positive direction and the right end is going in a negative direction.
Use the vertical line test...pass a vertical line from left to right across the graph. If you hit the graph more than once at a time, there is x-sharing, and it is not a function.
The phase angle phi in the cosine function cos(wtphi) affects the horizontal shift of the graph of the function. A positive phi value shifts the graph to the left, while a negative phi value shifts it to the right.
An even function is symmetric about the y-axis. The graph to the left of the y-axis can be reflected onto the graph to the right. An odd function is anti-symmetric about the origin. The graph to the left of the y-axis must be reflected in the y-axis as well as in the x-axis (either one can be done first).