Question

Given a polynomial function f(x) = –x2 + 2x + 1 and an exponential function g(x) = 2x, what key features do f(x) and g(x) have in common?

A.)Both f(x) and g(x) decrease over the interval of [1 , ∞).
B.) Both f(x) and g(x) have the same range of (–∞, 2).
C.) Both f(x) and g(x) have the same x-intercept of (–1, 0).
D.)Both f(x) and g(x) have the same y-intercept of (0, 1).

Answer 1

The only key feature that these functions have in common is that they have the same y-intercept. So the correct option is D.

What do these functions have in common?

Here we have the functions:

$f(x) = -x^2 + 2x + 1\\\\g(x) = 2^x$

f(x) is quadratic, and g(x) is exponential.

Notice that the exponential function has a positive base, so it is increasing. For the quadratic equation we can see a negative leading coefficient, so it opens downwards.  So first and second options are false.

Also, g(x) never intersects the x-axis, so third option is false.

Finally, the y-intercepts of the given functions are:

$f(0) = -0^2 + 2*0 + 1 = 1\\\\g(0) = 2^0 = 1$

So the y-intercepts are equal, meaning that the correct option is D.

If you want to learn more about y-intercepts:

https://brainly.com/question/24363347

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