Question

use the given interactions to edit the selected curve.

Explanation:

Step1: Identify the transformation parameters

The given parameters are: Vertical Stretching/Shrinking \( c = 1 \), Horizontal Stretching/Shrinking \( c = 1 \), Vertical Shift \( = 8 \), Horizontal Shift \( = 0 \), Reflect over x - axis (not checked), Reflect over y - axis (not checked), Base \( = 5 \).

Step2: Recall the general form of a logarithmic function transformation

The general form of a transformed logarithmic function is \( y = c\log_{b}(x - h)+k \), where \( b \) is the base, \( h \) is the horizontal shift, \( k \) is the vertical shift, and \( c \) is the vertical stretch/shrink factor. If we reflect over the x - axis, we have a negative sign in front of \( c \), and reflection over the y - axis would change \( x\) to \( -x \) inside the logarithm.

Here, \( b = 5 \), \( h = 0 \), \( k = 8 \), \( c = 1 \), no reflections. So the function is \( y=\log_{5}(x)+8 \) (since horizontal shift \( h = 0 \), so \( x - h=x-0 = x\)).

Step3: Analyze the graph (if we were to sketch it)

The parent function \( y = \log_{5}(x) \) has a vertical asymptote at \( x = 0 \), passes through \( (1,0) \) and \( (5,1) \). After a vertical shift up by 8 units, the vertical asymptote remains at \( x = 0 \), and the point \( (1,0) \) moves to \( (1,8) \), the point \( (5,1) \) moves to \( (5,9) \). Since there is no horizontal or vertical stretch/shrink ( \( c = 1 \) for both) and no reflections, the shape of the logarithmic curve (increasing, since the base \( 5>1 \) and no reflection over x - axis) with a vertical shift up by 8 units is what we get.

Answer:

The equation of the transformed logarithmic curve is \( y=\log_{5}(x)+8 \)