the graph shows the function y=1/x-h + k . determine whether the value of each constant h and k is positive negative or zero explain your reasoning.
h is the horizontal shift
k is the vertical shift
Well, well, well, aren't we having some mathematical fun here? Let's analyze these constants, h and k, shall we?
First up, let's talk about h. If h is positive, then that means we are shifting the graph horizontally to the right. If h is negative, it shifts the graph to the left. And if h is zero, well, then the graph isn't going anywhere horizontally, it's just chillin' where it is.
Now, let's tackle k. If k is positive, we are moving the graph upwards. If k is negative, the graph takes a downward turn. Lastly, if k is zero, it means the graph isn't moving vertically, it's maintaining its current height.
So, to sum it up:
- If h is positive, the graph moves rightwards. Negative? Leftwards. Zero? No horizontal movement.
- If k is positive, the graph moves up. Negative? It goes down. Zero? No vertical changes.
Hope that brings a smile to your mathematical face!
To determine the signs of the constants h and k in the equation y = 1/x - h + k, we need to analyze the behavior of the graph.
First, let's consider the constant h. In the equation y = 1/x - h + k, the value of h is subtracted from 1/x. When h is positive, it will shift the graph downward by h units. Similarly, when h is negative, it will shift the graph upward by h units. If h is zero, it will have no effect on the graph's vertical position.
Next, let's discuss the constant k. In the equation y = 1/x - h + k, the value of k is added to the expression 1/x - h. When k is positive, it will shift the graph upward by k units. If k is negative, it will shift the graph downward by k units. When k is zero, it will not affect the graph's vertical position.
In summary:
1. The constant h will determine the vertical position of the graph. Positive h will shift it downward, negative h will shift it upward, and if h is zero, there will be no vertical shift.
2. The constant k will also determine the vertical position of the graph. Positive k will shift it upward, negative k will shift it downward, and if k is zero, there will be no vertical shift.
Please note that these explanations are based on the general behavior of the equation. To have a more accurate analysis, it is essential to consider specific x and y values or points on the graph.
To determine the values of the constants h and k in the function y = 1/x - h + k and whether they are positive, negative, or zero, we need to analyze their effects on the graph.
Let's start with h:
1. If h is positive: Adding a positive value to x in the denominator, the function will shift to the right along the x-axis. The graph will move horizontally.
2. If h is negative: Adding a negative value to x in the denominator, the function will shift to the left along the x-axis. The graph will move horizontally.
3. If h is zero: Setting h to zero means there is no adjustment to the x-values in the denominator. The graph will not move horizontally.
Now let's consider k:
1. If k is positive: Adding a positive value to the entire function will shift the graph upward along the y-axis. The graph will move vertically.
2. If k is negative: Adding a negative value to the entire function will shift the graph downward along the y-axis. The graph will move vertically.
3. If k is zero: Setting k to zero means there is no adjustment to the function vertically. The graph will not move vertically.
In conclusion:
- The value of h affects the horizontal position of the graph. h > 0 shifts it to the right, h < 0 shifts it to the left, and h = 0 keeps it unchanged horizontally.
- The value of k affects the vertical position of the graph. k > 0 shifts it upward, k < 0 shifts it downward, and k = 0 keeps it unchanged vertically.