Question

15.
the graph has points (0, -1), (1, -2), (2, -4) and is a curve on the coordinate plane with x and y axes.

Explanation:

Assuming the problem is to find the equation of the exponential function (since the graph looks like an exponential decay curve). Let's assume the general form of an exponential function is \( y = ab^x \).

Step1: Use the point (0, -1)

Substitute \( x = 0 \), \( y = -1 \) into \( y = ab^x \). We know that \( b^0 = 1 \), so \( -1 = a\times1 \), which gives \( a = -1 \).

Step2: Use the point (1, -2)

Now we know \( a = -1 \), substitute \( x = 1 \), \( y = -2 \), and \( a = -1 \) into \( y = ab^x \). So \( -2 = -1\times b^1 \), which simplifies to \( -2 = -b \). Solving for \( b \), we get \( b = 2 \).

Step3: Write the equation

Now that we have \( a = -1 \) and \( b = 2 \), the equation of the function is \( y = -1\times2^x \) or \( y = -2^x \).

Answer:

The equation of the function is \( y = -2^x \)