Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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).

Sagot :

facundo3141592

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:

[tex]f(x) = -x^2 + 2x + 1\\\\g(x) = 2^x[/tex]

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:

[tex]f(0) = -0^2 + 2*0 + 1 = 1\\\\g(0) = 2^0 = 1[/tex]

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

#SPJ1

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.