Y=0 would be a horizontal line. An asymptote is a line that a function approaches, but never reaches. Exponential functions such as these are a smooth curve. If both numbers are positive numbers greater than or equal to 1, the curve increases. If at least one of the numbers is a positive number between 0 and 1, the curve decreases. If <em>a</em> is a negative number, the curve decreases as well. If either <em>a</em> or <em>b</em> is zero, then the graph would stay constant at 0. However, as long as neither <em>a</em> nor <em>b</em> is zero, then this graph will never touch that point. The only way to get an answer of y=0 is to multiply by 0. If neither <em>a</em> nor <em>b</em> is zero, this won't happen.
To solve A, complete the square for both variables.
The center is (6,4)
9514 1404 393
Answer:
Step-by-step explanation:
The ratios all have ...
first number : second number = 1 : 4
Using first numbers of 1, 2, 3, the second numbers can be found by multiplying these by 4. (1, 4), (2, 8), (3, 12)
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You plot these (x, y) points the same way you plot <em>any</em> point on a coordinate grid. The first (x) value is the horizontal distance from the vertical axis. Positive is to the right. The second (y) value is the vertical distance from the horizontal axis. Positive is up.
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Of course, the origin is where the horizontal and vertical axes meet. It can be convenient to find one of the coordinates on its respective axis, then use the other coordinate to find the point at the desired distance from that axis.
Usually, you would choose the axis on the basis of how easy it is to determine exactly where the coordinate lies. If the y-axis is marked every 5, for example, it might be hard to determine where a multiple of 4 will lie. Locating the x-coordinate on the x-axis may be an easier way to start.