Question

question 8 (1 point)
which of the following functions would translate horizontally 4 units to the left?

a) ( f(x)=log_{10}(x - 4) )

b) ( f(x)=4log_{10}x )

c) ( f(x)=log_{10}x + 4 )

d) ( f(x)=log_{10}(x + 4) )

Explanation:

Step1: Recall Horizontal Shift Rule

For a function \( y = f(x) \), the transformation \( y = f(x + h) \) shifts the graph horizontally. If \( h>0 \), it shifts left by \( h \) units; if \( h<0 \), it shifts right by \( |h| \) units.

Step2: Analyze Each Option

• Option a: \( f(x)=\log_{10}(x - 4) \). Here, \( h=-4 \), so it shifts right 4 units.
• Option b: \( f(x)=4\log_{10}x \). This is a vertical stretch, not a horizontal shift.
• Option c: \( f(x)=\log_{10}x + 4 \). This is a vertical shift up 4 units, not horizontal.
• Option d: \( f(x)=\log_{10}(x + 4) \). Here, \( h = 4>0 \), so it shifts left 4 units.

Answer:

d) \( f(x)=\log_{10}(x + 4) \)