Q: Which of the following best describes the end behavior of $$f(x) = x^2$ + 1$$?

As $$x \to \infty$$, $$f(x) \to \infty$$; as $$x \to -\infty$$, $$f(x) \to \infty.$$

Question 1

Which sequence of transformations will convert the graph of $$y = x^2$ to the graph of y$$ = $$x^2 + 1$?

Accepted Answer

Shift the graph of $$y = x^2$ up by 1 unit.

Question 2

What is the domain of the function $$f(x) = x^2$ + 1$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 3

What is the range of the function $$f(x) = x^2$ + 1$$?

Accepted Answer

$$[1, \infty)$$

Question 4

What is the equation of the axis of symmetry for the function $$f(x) = x^2$ + 1$$?

Accepted Answer

$$x = 0$$

Question 5

Suppose you want to graph $$y = x^2$ + 1$$ starting from $$y = x^2$. Which transformation should you apply first?

Accepted Answer

Vertical translation upward by 1 unit.

Question 6

If the graph of $$y = x^2$ is shifted up by 1 unit, what is the new vertex of the parabola?

Accepted Answer

$$(0, 1)$$

Question 7

Which of the following best describes the end behavior of $$f(x) = x^2$ + 1$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o \infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty.$$

Question 8

Which real-world scenario can be modeled by $$f(x) = x^2$ + 1$$?

Accepted Answer

The height (in meters) of a ball thrown upward from a platform 1 meter above the ground, where $$x is $$time in seconds and the ball's height increases quadratically.

Question 9

If $$f(x) = x^2$ + 1$$, what is $$f(-3)$$?

Accepted Answer

$$10$$

Question 10

Which of the following statements is true about the vertex of $$f(x) = x^2$ + 1$$?

Accepted Answer

It is the minimum point of the graph.

Question 11

Given $$f(x) = x^2$ + 1$$, which of the following is the $$y-$$intercept?

Accepted Answer

$$(0, 1)$$

Question 12

Which transformation would change $$y = x^2$ + 1 to$$ $$y = (x - 2)^2$ + 1$$?

Accepted Answer

Shift the graph right by 2 units.

Question 13

If $$f(x) = x^2$ + 1$$, for which value of $$x$$ does $$f(x) = 10$$?

Accepted Answer

$$x = 3 or$$ $$x = -3$$

Question 14

Which of the following best describes the symmetry of the graph of $$f(x) = x^2$ + 1$$?

Accepted Answer

It is symmetric about the $$y-$$axis.

Question 15

If the function $$f(x) = x^2$ + 1$$ models the cost (in dollars) to produce $$x$$ units of a product, what is the minimum possible cost?

Accepted Answer

$$1$$

Transformations and Analysis of Exponential Functions

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