Range of a Function from its Graph

Submitted by petr.beremlijski on Tue, 10/22/2024 - 13:42

Project ID:

7360000058

Accepted:

SubArea:

Properties of functions

Type:

Scrolling

Layout:

6x6

Question:

Use the given graphs to determine the ranges of corresponding functions. Match every given function to its range. (Dashed lines represent asymptotes of functions.)

Questions Title:

Graphs:

Answers Title:

Ranges:

Question 1:

f_{1} (x) = 3 e^{- x^{2}} - 1

Question 1 Image:

Answer 1:

$(- 1; 2]$

Question 2:

f_{2} (x) = {\begin{cases} - 0.5 (x + 4)^{2} + 4; & x \in (- \infty; - 2] \\ 0.5 (x - 4)^{2} - 4; & x \in [- 2; \infty) \end{cases}

Question 2 Image:

Answer 2:

$R$

Question 3:

f_{3} (x) = {\begin{cases} - \frac{8}{x + 2} + 2; & x \in (- \infty; - 2) \\ \frac{8}{x - 2} + 2; & x \in (2; \infty) \end{cases}

Question 3 Image:

Answer 3:

$(2; \infty)$

Question 4:

f_{4} (x) = {\begin{cases} - \frac{8}{x} + 2; & x \in (- \infty; 0) \\ - \frac{8}{x} - 2; & x \in (0; \infty) \end{cases}

Question 4 Image:

Answer 4:

$(- \infty; - 2) \cup (2; \infty)$

Question 5:

f_{5} (x) = {\begin{cases} \log_{2} (x + 2) + 1; & x \in (- 2; 0) \\ \log_{2} (- x + 2) + 1; & x \in [0; 2) \end{cases}

Question 5 Image:

Answer 5:

$(- \infty; 2]$

Question 6:

f_{6} (x) = 2; x \in (0; \infty)

Question 6 Image:

Answer 6:

${2}$

Range of a Function from its Graph

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