a function is defined by the equation y=8x-3. If the domain is 2≤x≤4, find the minimum value in the range of the function.
since it is a straight line with positive slope of 8, the lowest x is the lowest value of y
if x = 2 then y = 16-3 = 13
so 13
To find the minimum value in the range of the function, we need to evaluate the function for all values within the given domain and find the smallest result.
The given function is y = 8x - 3.
First, let's substitute the lower limit of the domain (x = 2) into the equation to find the corresponding y-coordinate:
y = 8(2) - 3
y = 16 - 3
y = 13
Therefore, when x = 2, y = 13.
Next, let's substitute the upper limit of the domain (x = 4) into the equation:
y = 8(4) - 3
y = 32 - 3
y = 29
Therefore, when x = 4, y = 29.
Now we compare the values of y for both limits of the domain. The smallest value is the minimum value in the range of the function, which is y = 13.
So, the minimum value in the range of the function is 13.
To find the minimum value in the range of the function, we need to determine the minimum value of y given the domain.
Given the equation y = 8x - 3, let's substitute the lowest value of the domain (x = 2) into the equation:
y = 8(2) - 3
y = 16 - 3
y = 13
Now, let's substitute the highest value of the domain (x = 4) into the equation:
y = 8(4) - 3
y = 32 - 3
y = 29
Therefore, the range of the function within the given domain is 13 ≤ y ≤ 29.
The minimum value in the range is 13.