True or false: If a is any positive real number, the graph of y=a^x will go through the point (0,1).
True or false: x^3+2x^2 is an exponential equation because it contains exponents.
I got true for both of them is that right?
true, false
if x has powers, it is a polynomial.
If x is the power, it is an exponential, as in e^x
polynomials have constant powers of a variable.
exponentials have variable powers of a constant.
For the first question, you are correct. If we substitute x=0 into the equation y=a^x, we get y=a^0, which simplifies to y=1. This means the graph of y=a^x will go through the point (0,1) for any positive real number a.
For the second question, you are not correct. An exponential equation is a type of equation in which the variable appears as an exponent. In the given equation, x^3+2x^2, the variable x appears with exponents, but it is not in the form of an exponential equation. It is a polynomial equation since the highest exponent of x is 3.
The statement "If a is any positive real number, the graph of y=a^x will go through the point (0,1)" is true. This is because any positive real number raised to the power of zero is always equal to 1.
The statement "x^3+2x^2 is an exponential equation because it contains exponents" is false. An exponential equation is one in which the variable is in the exponent, such as y = a^x. In the given equation, x^3+2x^2, the variable is not in the exponent, so it is not an exponential equation.