Rational functions

9000007607

Level:

Find the range of the function

f (x) = 2 - \frac{3}{x - 2}

R ∖ {2}

R ∖ {- 2}

R ∖ {- 2; 3}

(0; \infty)

R

9000007702

Level:

Identify a correct statement which concerns the function

f (x) = \frac{1}{- x + 2}

None of the statements above is true.

The function

f

is an increasing function.

The function

f

is bounded below.

The function

f

has a maximum at

x = 2

The function

f

is decreasing on

(2; \infty)

9000007707

Level:

Identify a correct statement which concerns the function

f (x) = 2 - \frac{1}{x}

None of the statements above is true.

The function

f

is bounded above.

The function

f

is an even function.

The function

f

is a bounded function.

The function

f

is an odd function.

9000007709

Level:

Identify a correct statement which concerns the function

f (x) = - \frac{5}{x} - 3

None of the statements above is true.

The function

f

is bounded above.

The function

f

is an even function.

The function

f

is a decreasing function on

(0; \infty)

The function

f

is an odd function.

9000014201

Level:

Find intersection points of the graph of the rational function

f (x) = \frac{2 x - 3}{x - 2}

with

y

-axis.

Y = [0; \frac{3}{2}]

Y = [\frac{3}{2}; 0]

Y_{1} = [0; \frac{3}{2}] and Y_{2} = [\frac{3}{2}; 0]

Y = [2; 2]

9000014202

Level:

Find the intersections of the graph of the rational function

f (x) = \frac{x + 2}{2 - x}

with

x

-axis.

X = [- 2; 0]

X = [0; - 2]

X_{1} = [0; - 2] and X_{2} = [- 2; 0]

X = [2; 0]

9000014203

Level:

Which of the statements from the following list is true for the function

f (x) = - \frac{2}{x} + 1

The function

f

is a one-to-one function.

The function

f

is an odd function.

The function

f

is an increasing function.

The graph of the function

f

is a hyperbola with branches in the second and fourth quadrant.

9000014206

Level:

Find the domain

Dom (f)

and range

Ran (f)

of the function

f (x) = \frac{2 + x}{x + 4}

\begin{aligned} Dom (f) & = (- \infty; - 4) \cup (- 4; \infty), \\ Ran (f) & = (- \infty; 1) \cup (1; \infty) \end{aligned}

\begin{aligned} Dom (f) & = (- \infty; 4) \cup (4; \infty), \\ Ran (f) & = (- \infty; 1) \cup (1; \infty) \end{aligned}

\begin{aligned} Dom (f) & = (- \infty; 2) \cup (2; \infty), \\ Ran (f) & = (- \infty; 4) \cup (4; \infty) \end{aligned}

\begin{aligned} Dom (f) & = (- \infty; 4) \cup (4; \infty), \\ Ran (f) & = (- \infty; 2) \cup (2; \infty) \end{aligned}

9000014207

Level:

Identify a possible analytic expression for the function

f

graphed in the picture.

f (x) = \frac{x + 1}{x + 2}

f (x) = \frac{1}{x + 2} - 1

f (x) = \frac{1}{x + 2} + 1

f (x) = \frac{x + 1}{x - 2}

9000014208

Level:

Identify a possible analytic expression for the function

f

graphed in the picture.

f (x) = \frac{2 x + 1}{x - 1}

f (x) = \frac{3}{x - 1} - 2

f (x) = \frac{2 x - 1}{x + 1}

f (x) = \frac{2 x + 2}{x - 1}

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