Given the parent function f(x)log(base10)x, state the equation of the function that results from a vertical stretch by a factor of 2/5, a horizontal stretch by a factor of 3/4, a reflection in the y-axis , a horizontal translation 2 units to the right, and a vertical translation 3 units down.
I did this so far and I don't know what to write for a horizontal stretch by a factor of 3/4.
f(x)=alog(base10)(k(x-d))+c
=2/5log(base10)(-k(x-2))-3
Would it be 3/4 or different I know it says 1/k?
To determine the equation of the function resulting from a horizontal stretch by a factor of 3/4, we need to consider the formula for horizontal stretches in the form: f(x) = a * log(base10)(k(x - d)) + c.
In this case, the horizontal stretch factor is given as 3/4. The formula for a horizontal stretch by a factor of k is f(x) = a * log(base10)(kx) + c. So, we would substitute k = 3/4 into the formula.
Using the information you provided, the equation would be:
f(x) = (2/5) * log(base10)((3/4)(x - 2)) - 3
Please note that when performing transformations, it is necessary to adjust the values of the coefficients "a," "k," "d," and "c" accordingly.