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

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.

The function 𝑓 is given by 𝑓⁡(𝑥)=𝑒2⁢𝑥, and the function 𝑔 is given by 𝑔⁡(𝑥)=ln⁡(3⁢𝑥). For 𝑥>0, which of the following is an expression for 𝑓⁡(𝑔⁡(𝑥)) ? Responses9⁢𝑥29 x squared2⁢𝑥+ln⁡32 x plus ln 3(𝑒2⁢𝑥)·ln⁡(3⁢𝑥)open parentheses e to the power of 2 x end exponent close parentheses times ln open parentheses 3 x close parentheses

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

Which of the following options is equivalent to 32𝑎7𝑏3𝑐5?

In the general form of a logarithmic function 𝑓(𝑥)=log𝑏⁡(𝑥), what does 𝑏 represent?