Problemas
Write the equation that models the function described. Shifts the parent function, y=log_(3)x 7 units left and reflects across the x-axis. y=-log_(3)(x+7) y=-log_(3)(x-7) y=-7log_(3)x y=7-log_(3)x y=-7-log_(3)x
Roztwór
Jesús
maestro · Tutor durante 5 años
4
(265 Votos)
Respuesta
The equation that models the function described is \(y = -\log_{3}(x + 7)\).
Explicación
## Step 1The problem involves the transformation of the parent function
. The transformations are a shift of 7 units to the left and a reflection across the x-axis.## Step 2The shift of the function 7 units to the left is represented by the transformation
. This is because shifting a function to the left is achieved by replacing
with
, where
is the number of units the function is to be shifted.## Step 3The reflection of the function across the x-axis is represented by the transformation
. This is because reflecting a function across the x-axis is achieved by multiplying the function by -1.## Step 4Combining the transformations from steps 2 and 3, we get the transformed function as \(y = -\log_{3}(x + 7)\).