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How does the graph of an exponential function differ from the graph of a linear function and how is the rate of change different?
The graph of a linear function is a line with a constant slope. The graph of an exponential function is a curve with a non-constant slope. The slope of a given curve at a specified point is the derivative evaluated at that point.
How do you get the tangent line without the graph?
The answer will depend on the context. If the curve in question is a differentiable function then the gradient of the tangent is given by the derivative of the function. The gradient of the tangent at a given point can be evaluated by substituting the coordinate of the point and the equation of the tangent, though that point, is then given by the point-slope equation.
How would you explain to a seventh grader the difference between the domains of an odd root radical function and an even root radical function?
To start with, when you multiply an even number of negative numbers, the answer is positive. When you multiply an odd number of negative numbers, the answer is negative. When you multiply any number of positive numbers, the answer is always positive. For positive numbers, the value of a power is always positive. For negative numbers, the value of an odd power is negative, and the value of an even power is positive. Finding roots is the inverse of taking powers, so that an odd-root function can be evaluated for any value of x. An even-root function, however, cannot be evaluated when the value of x is negative, since an even power can never result in a negative answer. The domain of an odd root function is all real numbers; the domain of an even root function is the non-negative real numbers.
How many alternative solutions be evaluated?
3
What is the square root of Scotland?
A square root is a mathematical function whose argument must be a number - or an expression that can be evaluated so as to give a number. Since Scotland is neither a number nor an algebraic expression, the question makes no sense.
