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Q: The value of the determines whether the graph of an exponential function increases or decreases from left to right?

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If y is an exponential function of x then x is a logarithmic function of y - so to change from an exponential function to a logarithmic function, change the subject of the function from one variable to the other.

Yes.

Yes.

The graph of an exponential function f(x) = bx approaches, but does not cross the x-axis. The x-axis is a horizontal asymptote.

Yes, y = loga(x) means the same as x=ay.

Related questions

an exponential growth function describes an amount that increases exponentially over time.

An exponential function such as y=b^x increases as x goes to infinity for all values in the domain. That is, the function increases from left to right anywhere you look on the graph, as long as the base b is greater than 1. This is called a "Growth" function. However, the graph is decreasing as x goes to infinity if (a) the opposite value of the input is programmed into the function, as in y=b^-x, or if (b) the base is less than 1, as in y=(1/2)^x.

Yuo cannot include a graphical illustration here. Take a look at the Wikipedia, under "exponential function" and "logistic function". Basically, the exponential function increases faster and faster over time. The logistics function initially increases similarly to an exponential function, but then eventually flattens out, tending toward a horizontal asymptote.

True

The linear function increases by the same number each step. The exponential function increases more each step. (1,1),(2,2),(3,3) etc (1,1).(2,4),(3,9),(4,16), etc see how the second one increases a lot?

A linear function grows ( or shrinks) at a constant rate called its slope.An exponential function grows ( or shrinks) at a rate which increases(or decreases)over time. From a practical standpoint linear growth (or shrinkage) is simple and predictable. Exponential growth is essentially out of control and unsustainableand exponential decay soon becomes negligible.if y=az + b then y is a linear function of z. If y=aebz then y is an exponential function of z. If y= acbz then y is still an exponential function of z because you can substitute c=ek (so that k=logec) to give you y=aekbz .

Yes.

Yes.

A __________ function takes the exponential function's output and returns the exponential function's input.

The parent function of the exponential function is ax

No. The inverse of an exponential function is a logarithmic function.

As temperature increases, kinetic energy increases. As temperature decreases, kinetic energy decreases. Temperature is directly proportional to kinetic energy.

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