In the 𝑥𝑦-plane, the graph of a rational function 𝑓 has a hole at 𝑥=2. Input values of 𝑓 sufficiently close to 2 correspond to output values arbitrarily close to 6. Which of the following could define 𝑓𝑥 ?Responses 𝑓𝑥=6𝑥-2𝑥+3𝑥-3𝑥-2f open parentheses x close parentheses equals fraction numerator 6 open parentheses x minus 2 close parentheses open parentheses x plus 3 close parentheses over denominator open parentheses x minus 3 close parentheses open parentheses x minus 2 close parentheses end fraction 𝑓𝑥=𝑥-2𝑥+4𝑥-2𝑥-1f open parentheses x close parentheses equals fraction numerator open parentheses x minus 2 close parentheses open parentheses x plus 4 close parentheses over denominator open parentheses x minus 2 close parentheses open parentheses x minus 1 close parentheses end fraction 𝑓𝑥=𝑥-6𝑥+4𝑥-6𝑥-1f open parentheses x close parentheses equals fraction numerator open parentheses x minus 6 close parentheses open parentheses x plus 4 close parentheses over denominator open parentheses x minus 6 close parentheses open parentheses x minus 1 close parentheses end fraction

The function 𝑓 is given by 𝑓⁡(𝑥)=2(3⁢𝑥). Which of the following statements describes characteristics of the graph of 𝑓 in the 𝑥⁢𝑦-plane?ResponsesThe graph of 𝑓 is a vertical dilation of 𝑦=2𝑥, and 𝑓⁡(𝑥) is equivalent to 8𝑥.The graph of  f  is a vertical dilation of  y equals 2 to the power of x , and  f open parentheses x close parentheses  is equivalent to  8 to the power of x .The graph of 𝑓 is a vertical dilation of 𝑦=2𝑥, and 𝑓⁡(𝑥) is equivalent to 8·2𝑥.The graph of  f  is a vertical dilation of  y equals 2 to the power of x , and  f open parentheses x close parentheses  is equivalent to  8 times 2 to the power of x .The graph of 𝑓 is a horizontal dilation of 𝑦=2𝑥, and 𝑓⁡(𝑥) is equivalent to 8𝑥.The graph of  f  is a horizontal dilation of  y equals 2 to the power of x , and  f open parentheses x close parentheses  is equivalent to  8 to the power of x .The graph of 𝑓 is a horizontal dilation of 𝑦=2𝑥, and 𝑓⁡(𝑥) is equivalent to 8·2𝑥.

In the 𝑥𝑦-plane, the function ℎ, given by ℎ𝑥=3𝑥+2, is a horizontal translation of the exponential function 𝑓, given by 𝑓𝑥=3𝑥. Which of the following is an equivalent form for ℎ𝑥 that expresses ℎ as a vertical dilation of 𝑓 ?Responsesℎ𝑥=3𝑥/2h open parentheses x close parentheses equals 3 to the power of open parentheses x divided by 2 close parentheses end exponentℎ𝑥=9·3𝑥h open parentheses x close parentheses equals 9 times 3 to the power of x ℎ𝑥=9·13𝑥h open parentheses x close parentheses equals 9 times open parentheses 1 third close parentheses to the power of x

QUESTION 4Given: and𝑓(𝑥) = 3𝑥−2 + 1 ℎ(𝑥) =− 1𝑥+524.1 Write down the equation of the asymptotes of 𝑓. (2)4.2 Determine the intercepts of𝑥 − 𝑓. (3)4.3 Determine the intercepts of𝑦 − 𝑓. (2)4.4 Sketch the graph of and on the same set of axes, clearly indicating𝑓 ℎthe distinctive features of the functions. (5)4.5 Determine the values for which𝑥 𝑓(𝑥) < ℎ(𝑥). (2)4.6 The line cuts at and . Write down the𝑦 =− 34 𝑥 + 254 𝑓 𝐸(3; 4) 𝐹coordinates of 𝐹. (7)

If (6,2) is a point on the graph of 𝑓(𝑥), give the coordinates of one point that must be on the graph of 𝑓−1(𝑥) if 𝑓−1(𝑥) exists.

Which of the following rational functions is graphed below?A.F(x) = 1(𝑥−4)2(x−4) 2 1​ B.F(x) = 1(𝑥+4)2(x+4) 2 1​ C.F(x) = 4𝑥2x 2 4​ D.F(x) = 14𝑥24x 2 1​ SUBMITarrow_backPREVIOUS