Question

9.

x	y
-1	-0.6
0	-6
1	-60
2	-600

Explanation:

Step1: Analyze the pattern between x and y

Let's check the ratio of consecutive y - values or the relationship between x and y. Let's assume the function is of the form \(y = ab^{x}+c\) or an exponential function. Let's check the ratios of \(y\) when \(x\) increases by 1.

From \(x=- 1\) to \(x = 0\): \(\frac{-6}{-0.6}=10\)

From \(x = 0\) to \(x = 1\): \(\frac{-60}{-6}=10\)

From \(x = 1\) to \(x = 2\): \(\frac{-600}{-60}=10\)

So the common ratio \(r = 10\). Now, when \(x = 0\), \(y=-6\). For an exponential function of the form \(y = ab^{x}\), when \(x = 0\), \(y=a\). So \(a=-6\) and \(b = 10\). Let's verify for \(x=-1\): \(y=-6\times10^{-1}=-6\times\frac{1}{10}=-0.6\), which matches. For \(x = 1\): \(y=-6\times10^{1}=-60\), which matches. For \(x = 2\): \(y=-6\times10^{2}=-600\), which matches. So the function is \(y=-6\times10^{x}\) or \(y=-6(10)^{x}\)

Step2: Confirm the function

We can write the general form of the exponential function as \(y = ab^{x}\), where \(a=-6\) (since when \(x = 0\), \(y=a\)) and \(b = 10\) (from the common ratio). So the equation of the function is \(y=-6\times10^{x}\)

Answer:

The function relating \(x\) and \(y\) is \(y = - 6\times10^{x}\) (or \(y=-6(10)^{x}\))