The graph if f is translated a whole number of units horizontally and vertically to obtain the graph of h
The function f is defined by
f(x)=x^2 write the expression for h(x)
The expression for h(x) is:
h(x) = (x-a)^2 + b,
where a is the horizontal translation (in whole number units) and b is the vertical translation (in whole number units).
Use the change of base formula to compute log6 base7
To compute log base 7 of 6 using the change of base formula, you can use the formula:
log base a of b = log base c of b / log base c of a
In this case, we want to compute log base 7 of 6, so a=7 and b=6. Let's choose c=10 to compute the logs:
log base 7 of 6 = log base 10 of 6 / log base 10 of 7
To calculate these logs using a calculator:
log base 10 of 6 ≈ 0.7781512504
log base 10 of 7 ≈ 0.84509804001
Now, substitute these values into the above equation:
log base 7 of 6 ≈ 0.7781512504 / 0.84509804001 ≈ 0.9190780924
Therefore, log base 7 of 6 ≈ 0.919.
The graph of the function of h for the intercept (2,4) and (-4,-2) write the domain and range
The domain is the set of all possible x-values for the function h. In this case, since we are given two points (2,4) and (-4,-2), we can determine that the domain of h is all real numbers.
The range is the set of all possible y-values for the function h. By looking at the given points (2,4) and (-4,-2), we can see that the y-values of h range from -2 to 4. Therefore, the range of h is [-2, 4].
To translate the graph of f(x)=x^2 horizontally by a whole number of units, we can use the following expression for h(x):
h(x) = (x - a)^2
where 'a' represents the horizontal translation.
To translate the graph of f(x)=x^2 vertically by a whole number of units, we can use the following expression for h(x):
h(x) = x^2 + b
where 'b' represents the vertical translation.
Combining these two translations, the expression for h(x) becomes:
h(x) = (x - a)^2 + b
To obtain the expression for h(x), we need to translate the graph of f(x)=x^2 horizontally and vertically.
Let's start with the horizontal translation. If we want to shift the graph horizontally by a whole number of units, we need to subtract or add that number inside the function. Let's say we want to shift it by a number, c, units to the right. The expression for the horizontal translation of f(x) is then f(x - c).
Next, let's consider the vertical translation. If we want to shift the graph vertically by a whole number of units, we need to subtract or add that number outside the function. Let's say we want to shift it by a number, d, units upward. The expression for the vertical translation of f(x) is then f(x) + d.
Putting it all together, the expression for h(x) can be written as follows:
h(x) = f(x - c) + d
In this specific case, where f(x) = x^2, the expression for h(x) will be:
h(x) = (x - c)^2 + d
Note that the variables c and d represent the number of units the graph is shifted horizontally and vertically, respectively.