This table shows the input and output values for an exponential function f(x) .

Mathematics

2 answers:

Gre4nikov [31]2 years ago

8 0

The correct answer is: [B]: "4 " .
______________________________________
Explanation:
______________________________________
Refer to the table (provided within the actual question).

Note that the "inputs" ; or "x-values" ; are all listed in "chronological order" ; and are all "one (1) unit apart. and range from: "x = -3" to "x = 3" .

When "x = 0" ; the "output" ; or "f(x)" is "1/4" .
When "x = 1" ; the "output" ; or "f(x)" is: "1" .
_________________________________________________
So; the ratio of these two "outputs" is: "¼ : 1" ; or, write as:
 " (¼) / 1 " ; and note that: " (¼) / 1 = (¼) ÷ 1 = ¼.

However; note that: "1/4" ; or "1:4" is NOT among the [answer choices given].

However, the ratio of the 2 (two) corresponding "outputs"; chronologically,
going from when "x = 1" ; to "x = 0" ; is: "1 : ¼" ; or; write as: "1 / (¼)" ;

And note that: "1 / (¼)" = " 1 ÷ (¼) " = 1 * (4/1) = 1 * 4 = "4" .

This corresponds to: Answer choice: [B]: "4" .
_________________________________________________
Let us further confirm that this answer is correct:
_________________________________________________
When x = 3; the "output" is: "16" .

When x = 2; the "output" is: "4" .

The ratio: "16/4 = ? 4 ? " ; → Yes!
_________________________________________________
When x = 2; the "output" is: "4" .

When x = 1; the "output" is: "1" .

The ratio: "4/1 = ? 4 ? " ; → Yes!
_________________________________________________
When x = 1; the "output" is: "1" .

When x = 0; the "output" is: "(¼)" .

The ratio: "1 / (¼) = ? 4 ? " ;

→ "1 / (¼)" = " 1 ÷ (¼) " = 1 * (4/1) = 1 * 4 = "4" . YES!
________________________________________________
When x = 0; the "output" is: "(¼)" .

When x = -1; the "output" is: "(¹/₁₆)" .

The ratio: "(¼) / (¹/₁₆) = ? 4 " ? ;

→ "(¼) / (¹/₁₆) = "(¼) ÷ (¹/₁₆) " = "(¼) * (¹⁶/₁) = (1*16) / (4*1) = 16/4 = "4" . Yes!
________________________________________________________
When x = -1; the "output" is: "(¹/₁₆)" .

When x = -2; the "output" is: "(¹/₆₄)" .

The ratio: "(¹/₁₆) / (¹/₆₄) = ? 4 " ? ;

→ "(¹/₁₆) / (¹/₆₄) = "(¹/₁₆) ÷ (¹/₆₄)" = "(¹/₁₆) * (⁶⁴/₁)" = (1*64) / (16*1) = 64/16 = "4" . Yes!
__________________________________________________________
When x = -2; the "output" is: "(¹/₆₄)" .

When x = -3; the "output" is: "(¹/₂₅₆)" ,

The ratio: "(¹/₆₄)/(¹/₂₅₆) = ? 4 " ? ;

→ "(¹/₆₄) / (¹/₂₅₆)" ;

= " (¹/₆₄) ÷ (¹/₂₅₆)" = " (¹/₆₄) * (²⁵⁶/₁) " = (1*256) / (64*1) = 256/164 = "4 " . Yes!
__________________________________________________________
→ So; as calculated; the ratio is: "4" ; which is:
__________________________________________________________
→ Answer choice: [B]: "4" .
__________________________________________________________