c. In the context of the problem, if R(x) = 10, it means that the function R has a constant value of 10 for all values of x. It represents a horizontal line on a graph at a height of 10.
d. If 2R(x) is taken, it means that the function R is multiplied by 2. This would result in scaling the original function vertically by a factor of 2, effectively doubling the values of R(x) for each x.
When comparing 2R(x) with R(2x), the latter represents evaluating the function R at 2x. In other words, the input value for the function is doubled. The two expressions are not the same, as 2R(x) involves doubling the output of R(x), while R(2x) involves doubling the input value of R.
e. R(2x) - R(x) means evaluating the function R at 2x and subtracting the value of R evaluated at x. It represents the difference between the outputs of R for the two different input values, 2x and x.
For the second part:
a. In the context of the problem, the function s(x) = x² describes a mathematical relationship where the input value x is squared. It represents a quadratic function.
b. s(9) means evaluating the function s at x = 9. Substituting the value 9 into the function, we have s(9) = 9² = 81. It represents the result of squaring the value 9.
c. If s(x) = 9, it means finding the value of x that, when squared, equals 9. In this context, it represents finding the square root of 9, which is x = ±3. Therefore, s(x) = 9 represents the solutions x = 3 and x = -3.
d. 0.25s(9) means taking 0.25 (or 1/4) of the value s(9). Since s(9) = 81, multiplying it by 0.25 gives 0.25 * 81 = 20.25. So, 0.25s(9) equals 20.25 in this context.