write an equation for a rational function that has a vertical asymptote of -4, a horizontal asymptote of 3, and vertically shrinks the graph by a factor of 5 (compared to the graph of y=1/x).
So far I have Y=3x/x+4 but I can't figure out how to shrink the graph by 5.
if you have y = 3x(x+4), then shrink it by multiplying by 1/5
y = 3x / 5(x+4)
since 1/(5x) is shrunk compared to 1/x
To incorporate the vertical shrink of 5 into the equation, you can multiply the function by 1/5.
Start with the equation of the original function, y = 1/x.
To introduce the vertical asymptote at -4, we can modify the equation by replacing x with (x + 4) so that the denominator becomes zero at x = -4.
Now we have y = 1/(x + 4).
To account for the horizontal asymptote at y = 3, we can include the value 3 as a constant in the equation.
Now we have y = 3 + 1/(x + 4).
To finally shrink the graph by a factor of 5, multiply the entire function by 1/5.
Therefore, the equation of the rational function is:
y = (1/5) * (3 + 1/(x + 4)).
To shrink the graph of a rational function by a factor of 5, you need to divide the input variable by 5.
To achieve this, use the equation y = 3 / (5(x + 4)).
This equation will have a vertical asymptote at x = -4, a horizontal asymptote at y = 3, and shrink the graph by a factor of 5 compared to the graph of y = 1/x.